Hamiltonian Dynamical Systems and Applications:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherland
2008
|
| Schriftenreihe: | NATO Science for Peace and Security Series - B: Physics and Biophysics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 490 S. 235 mm x 155 mm |
| ISBN: | 9781402069628 1402069626 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV023356342 | ||
| 003 | DE-604 | ||
| 005 | 20080909 | ||
| 007 | t | ||
| 008 | 080623s2008 gw |||| 00||| eng d | ||
| 015 | |a 07,N48,0606 |2 dnb | ||
| 016 | 7 | |a 986280011 |2 DE-101 | |
| 020 | |a 9781402069628 |c Gb. : ca. EUR 192.55 (freier Pr.), ca. sfr 313.50 (freier Pr.) |9 978-1-402-06962-8 | ||
| 020 | |a 1402069626 |c Gb. : ca. EUR 192.55 (freier Pr.), ca. sfr 313.50 (freier Pr.) |9 1-402-06962-6 | ||
| 024 | 3 | |a 9781402069628 | |
| 028 | 5 | 2 | |a 11825104 |
| 035 | |a (OCoLC)633880971 | ||
| 035 | |a (DE-599)DNB986280011 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-355 | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 084 | |a 620 |2 sdnb | ||
| 245 | 1 | 0 | |a Hamiltonian Dynamical Systems and Applications |c ed. by Walter Craig |
| 264 | 1 | |a Dordrecht |b Springer Netherland |c 2008 | |
| 300 | |a XVII, 490 S. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a NATO Science for Peace and Security Series - B: Physics and Biophysics | |
| 650 | 0 | 7 | |a Hamiltonsches System |0 (DE-588)4139943-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |y 2007 |z Montreal |2 gnd-content | |
| 689 | 0 | 0 | |a Hamiltonsches System |0 (DE-588)4139943-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Craig, Walter |e Sonstige |4 oth | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016539877&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016539877 | ||
Datensatz im Suchindex
| _version_ | 1804137716779057153 |
|---|---|
| adam_text | Contents
Some aspects of finite-dimensional Hamiltonian dynamics
............. 1
D.V. Treschev
1
Symplectic structure. Invariant form of the Hamiltonian equations
1
1.1
Hamiltonian equations
............................. 1
1.2
The
Poisson
bracket
............................... 3
1.3
Liouville theorem on completely
integrable
systems
.... 4
2
A pendulum with rapidly oscillating suspention point
........... 5
3
Anti-integrable limit
....................................... 8
3.1
The standard map
................................. 8
3.2
Anti-integrable limit
............................... 9
3.3
Proof of the Aubry theorem
......................... 11
3.4
Some remarks
.................................... 12
4
Separatrix splitting
........................................ 13
4.1
Poincaré s
observation
............................. 13
4.2
The
Poincaré
integral
.............................. 14
4.3
Proof of Theorem
5................................ 15
4.4
Standard example
................................. 18
References
..................................................... 19
Four lectures on the N-body problem
............................... 21
Alain Chenciner
1
The
Poincaré-Birkhoff-Conley
twist map of the annulus
for the planar circular restricted three-body problem
............ 21
1.1
The Kepler problem as an oscillator
.................. 21
1.2
The restricted problem in the lunar case
............... 22
1.3
Hill s solutions
.................................... 24
1.4
The annulus twist map
............................. 26
2
The Arnold—Herman stability theorem for the spatial
(1 +
n)-body problem
...................................... 29
2.1
The secular Hamiltonian
............................ 30
2.2
Herman s normal form theorem and how to use it
....... 33
χ
Contents
2.3
A stability theorem
................................ 35
2.4
Herman s degeneracy
.............................. 36
3
Minimal action and Marchal s theorem
....................... 37
3.1
Central configurations and their
homographie
motions
... 37
3.2
Variational characterizations of Lagrange s equilateral
solutions
......................................... 38
3.3
Marchal s theorem
................................. 40
3.4
Minimization under symmetry constraints
............. 42
4
Global continuation via minimization
........................ 43
4.1
Bifurcations from the
Lagrange
equilateral relative
equilibrium
....................................... 44
4.2
From the equilateral triangle to the Eight
.............. 46
4.3
From the square to the Hip-Hop
..................... 48
4.4
The avatars of the regular
и
-gon
relative equilibrium:
eights, chains and generalized Hip-Hops
.............. 50
References
..................................................... 50
Averaging method and adiabatic invariants
.......................... 53
Anatoly Neishtadt
1 Introduction
.............................................. 53
2
Adiabatic
invariance
in one-frequency systems
................. 54
3
On adiabatic
invariance
in multi-frequency systems
............. 63
References
..................................................... 65
Transformation theory of Hamiltonian PDE and the problem
of water waves
.................................................. 67
Walter Craig
1
Hamiltonian systems
...................................... 67
2
Partial differential equations as Hamiltonian systems
............ 68
3
The problem of water waves
................................ 71
4
The Dirichlet-Neumann operator
............................ 73
5
Perturbation theory
........................................ 74
6
The calculus of transformations
............................. 75
References
..................................................... 82
Three theorems on perturbed KdV
................................. 85
Sergei B. Kuksin
1
KdV equation
............................................ 85
1.1
Integrabilityof(KdV)
.............................. 86
1.2
Normal forms for (KdV)
............................ 87
2
KAM-theory
............................................. 88
3
Averaging: Hamiltonian perturbations
........................ 89
4
Averaging: case of non-Hamiltonian perturbations
.............. 90
4.1
Deterministic perturbations
......................... 90
4.2
Random perturbations
.............................. 90
References
..................................................... 91
Contents xi
Groups and topology in the
Euler
hydrodynamics and KdV
............ 93
Boris Khesin
1
Euler
equations and geodesies
............................... 93
1.1
The
Euler
hydrodynamics equation
................... 93
1.2
Geodesies on Lie groups
............................ 94
1.3
Geodesic description for various equations
............ 95
2
Topology of steady flows
................................... 95
2.1
Arnold s classification of steady fluid flows
............ 95
2.2
Variational principles for steady flows
................ 97
3
Euler
equations and
integrable
systems
....................... 98
3.1
Hamiltonian reformulation of the
Euler
equations
....... 98
3.2
The Virasoro algebra and the KdV equation
........... 99
3.3
Equations-relatives and conservation laws
.............100
References
.....................................................101
Infinite dimensional dynamical systems and the Navier-Stokes equation
. 103
C. Eugene Wayne
1
First lecture: infinite dimensional dynamical systems
...........103
2
Second lecture: invariant manifolds for partial differential
equations on unbounded domains
............................
Ill
3
Third lecture: an introduction to the Navier-Stokes equations
.... 122
4
Fourth lecture: the long-time asymptotics of solutions
of the two-dimensional Navier-Stokes equation
................129
5
Conclusions
..............................................139
References
.....................................................140
Hamiltonian systems and optimal control
........................... 143
Andrei Agrachev
1
Introduction
..............................................143
2
First lecture
..............................................144
2.1
First order conditions
..............................145
3
Second lecture
............................................146
3.1
Second variation
..................................147
4
Third lecture
.............................................149
4.1
Curves in the
Lagrange Grassmannians...............150
4.2
Curvature-type invariants
...........................151
5
Fourth lecture
............................................153
References
.....................................................156
KAM
theory with applications to Hamiltonian partial
differential equations
............................................157
Xiaoping Yuan
1
Brief history and basic ideas of
KAM
theory
..................157
2
Derivation of the linearized equations
........................163
3
Solutions of the linearized equations
.........................167
4
Applications to partial differential equations
in higher dimensions
.................................·-----175
xii Contents
Appendix......................................................176
References.....................................................
176
Foor
lectures on
KAM
for the non-linear
Schrödinger
equation
.........179
L.H. Eliasson and S.B. Kuksin
1
The non-linear
Schrödinger
equation
........................179
1.1
The non-linear
Schrödinger
equation
.................179
1.2
An «»-dimensional Hamiltonian system
...............180
1.3
The topology
.....................................182
1.4
Action-angle variables
.............................183
1.5
Statement of the result
.............................184
1.6
KAM-tori
........................................185
1.7
Consequences of Theorem
1 ........................186
1.8
References
.......................................188
1.9
Notation
.........................................189
2
The homological equation
..................................190
2.1
Normal form Hamiltonians
.........................190
2.2
The KAM-iteration
................................191
2.3
The components of the homological equation
..........192
2.4
Small divisors and the second Melnikov condition
......194
3
Normal form Hamiltonians
.................................195
3.1
Blocks
...........................................195
3.2
Lipschitz domains
.................................197
3.3 Töplitz
at °o(d
= 2)................................199
3.4 Töplitz-Lipschitz
matrices (d
= 2)...................200
3.5
Normal form Hamiltonians
.........................201
4
Estimates of small divisors
.................................202
4.1
A basic estimate
...................................202
4.2
The second Melnikov condition (d
= 2)...............203
5
Functions with the
Töplitz-Lipshitz
property (d
= 2)...........208
5.1 Töplitz
structure of the Hessian
......................208
5.2 Töplitz-Lipschitz
matrices
Jžf x
Jžř
-»
gl(2,R)
.........209
5.3
Functions with the
Töplitz-Lipschitz
property
.........211
5.4
A short remark on the proof of Theorem
1.1...........211
References
.....................................................212
A Birkhoff normal form theorem for some
semilinear
PDEs
............213
D.
Bambusi
1
Introduction
..............................................213
2
Birkhoff s theorem in finite dimensions
.......................214
2.1
Statement
........................................214
2.2
Proof
............................................216
3
The case of PDEs
.........................................221
3.1
Hamiltonian formulation of the wave equation
.........221
3.2
Extension of Birkhoff s theorem to PDEs:
heuristic ideas
....................................223
Contents xiii
4
A
Birkhoff normal form
theorem for
semilinear PDEs...........224
4.1
Maps with localized coefficients and their properties
.... 224
4.2
Statement of the normal form theorem
and its consequences
...............................228
4.3
Application to the nonlinear wave equation
............229
5
Discussion
...............................................231
6
Proofs
...................................................231
6.1
Proof of the properties of functions with localized
coefficients
.......................................231
6.2
Proof of the Birkhoff normal form Theorem
4.3
and of its dynamical consequences
...................236
6.3
Proof of Proposition
4.2
on the verification
of the property of localization of coefficients
...........240
6.4
Proof of Theorem
4.4
on the nonresonance condition
.... 244
References
.....................................................246
Normal form of holomorphic dynamical systems
.....................249
Laurent Stolovitch
1
Definitions and examples
...................................249
1.1
Vector fields and differential equations
................250
1.2
Normal forms of vector fields
.......................253
1.3
Examples about linearization
........................256
1.4
Examples about nonlinearizable vector fields
.........,258
2
Holomorphic normalization
.................................259
2.1
Theorem of
A.D.
Brjuno
............................259
2.2
Theorems of J. Vey
................................261
2.3
Singular complete integrability-Main result
...........261
2.4
How to recover Brjuno s and Vey s theorems
from Theorem
2.3.6 ...............................268
2.5
Sketch of the proof
................................269
3
Proof of main Theorem
2.3.6................................273
3.1
Bounds for the cohomological equations
..............273
3.2
Iteration scheme
..................................277
3.3
Proof of the theorem
...............................278
4
Miscellaneous results
......................................280
4.1
Normal forms again
...............................280
4.2 KAM
theory
......................................281
4.3
Poisson
structures
.................................282
References
.....................................................283
Geometric approaches to the problem of instability in Hamiltonian
systems. An informal presentation
.................................285
Amadeu
Delshams, Marian Gidea, Rafael
de la Llave,
and
Tere
M.
Seara
1
Introduction
..............................................285
1.1
Two types of geometric programs
....................287
xiv Contents
2 Exposition
of the Arnold example
...........................289
2.1
The obstruction property
...........................291
2.2
Some final remarks on the example in [Arn64]
.........293
3
Return to a normally hyperbolic manifold. The two dynamics
approach
................................................294
3.1
The basics of the mechanism of return to a normally
hyperbolic invariant manifold
.......................294
3.2
The scattering map
................................296
3.3
The scattering map and homoclinic intersections
of submanifolds
...................................298
3.4
Monodramy
of the scattering map
....................299
3.5
Smoothness and smooth dependence on parameters
.....299
3.6
Geometric properties of the scattering map
............300
3.7
Calculation of the scattering map
....................301
4
The large gap model
.......................................303
4.1
Generation of intersections. Melnikov theory
for normally hyperbolic manifolds
...................304
4.2
Computation of the scattering map
...................307
4.3
The averaging method. Resonant averaging
............308
4.4
Repeated averaging
................................312
4.5
Invariant objects generated by resonances: secondary
tori, lower dimensional tori
.........................312
4.6
Heteroclinic intersections between the invariant objects
generated by resonances
............................315
5
The method of correctly aligned windows
.....................316
6
The large gap model: the method of correctly aligned windows
... 318
7
The large gap model in higher dimensions
.....................319
8
Instability caused by normally hyperbolic laminations
...........320
8.1
Models with two time scales: geodesic flows, billiards
with moving boundaries, Littlewood problems
.........321
References
.....................................................324
Appendix
......................................................330
Variational methods for the problem of Arnold diffusion
..............337
Chong-Qing Cheng
1
Introduction to Mather theory
...............................337
2
Existence of Homoclinic Orbits
.............................341
3
Pseudo-COnnecting Orbit Set
^η,μ,ψ
..........................342
4
Existence of heteroclinic orbits
..............................345
5
Construction of global connecting orbits
......................353
6
Application to a priori unstable systems
.......................364
References
.....................................................365
Contents xv
The calculus of variations and the forced pendulum
...................367
Paul H. Rabinowitz
1
Introduction
..............................................367
2
Periodic solutions
.........................................369
3
Heteroclinic solutions
......................................374
4
Multitransition solutions: the simplest case
....................380
5
Multitransition solutions: general case
........................387
6
The tip of the iceberg
......................................389
References
.....................................................390
Variational methods for Hamiltonian PDEs
..........................391
Massimiliano
Berti
1
Finite dimensions: resonant center theorems
...................391
1.1
The variational Lyapunov-Schmidt reduction
..........393
2
Infinite dimensions
........................................396
3
The variational Lyapunov-Schmidt reduction
..................397
3.1
The bifurcation equation
............................399
4
The small divisor problem
..................................402
5
The
(öl)-equation ........................................406
6
A variational principle on a Cantor set
........................408
7
Forced vibrations
.........................................412
7.1
The variational Lyapunov-Schmidt reduction
..........413
7.2
The bifurcation equation
............................414
References
.....................................................419
Spectral gaps of potentials in weighted Sobolev spaces
.................421
Jürgen Pöschel
1
Results
..................................................421
2
Reduction
................................................425
3
Gap Estimates
............................................426
4
Coefficient Estimates
......................................426
5
Modified Weights
.........................................428
References
.....................................................429
On the well-posedness of the periodic KdV equation
in high regularity classes
.........................................431
Thomas
Rappeler
and
Jürgen Pöschel
1
Results
..................................................431
2
Birkhoff Coordinates
......................................435
3
Regularity
...............................................438
References
.....................................................440
|
| adam_txt |
Contents
Some aspects of finite-dimensional Hamiltonian dynamics
. 1
D.V. Treschev
1
Symplectic structure. Invariant form of the Hamiltonian equations
1
1.1
Hamiltonian equations
. 1
1.2
The
Poisson
bracket
. 3
1.3
Liouville theorem on completely
integrable
systems
. 4
2
A pendulum with rapidly oscillating suspention point
. 5
3
Anti-integrable limit
. 8
3.1
The standard map
. 8
3.2
Anti-integrable limit
. 9
3.3
Proof of the Aubry theorem
. 11
3.4
Some remarks
. 12
4
Separatrix splitting
. 13
4.1
Poincaré's
observation
. 13
4.2
The
Poincaré
integral
. 14
4.3
Proof of Theorem
5. 15
4.4
Standard example
. 18
References
. 19
Four lectures on the N-body problem
. 21
Alain Chenciner
1
The
Poincaré-Birkhoff-Conley
twist map of the annulus
for the planar circular restricted three-body problem
. 21
1.1
The Kepler problem as an oscillator
. 21
1.2
The restricted problem in the lunar case
. 22
1.3
Hill's solutions
. 24
1.4
The annulus twist map
. 26
2
The Arnold—Herman stability theorem for the spatial
(1 +
n)-body problem
. 29
2.1
The secular Hamiltonian
. 30
2.2
Herman's normal form theorem and how to use it
. 33
χ
Contents
2.3
A stability theorem
. 35
2.4
Herman's degeneracy
. 36
3
Minimal action and Marchal's theorem
. 37
3.1
Central configurations and their
homographie
motions
. 37
3.2
Variational characterizations of Lagrange's equilateral
solutions
. 38
3.3
Marchal's theorem
. 40
3.4
Minimization under symmetry constraints
. 42
4
Global continuation via minimization
. 43
4.1
Bifurcations from the
Lagrange
equilateral relative
equilibrium
. 44
4.2
From the equilateral triangle to the Eight
. 46
4.3
From the square to the Hip-Hop
. 48
4.4
The avatars of the regular
и
-gon
relative equilibrium:
eights, chains and generalized Hip-Hops
. 50
References
. 50
Averaging method and adiabatic invariants
. 53
Anatoly Neishtadt
1 Introduction
. 53
2
Adiabatic
invariance
in one-frequency systems
. 54
3
On adiabatic
invariance
in multi-frequency systems
. 63
References
. 65
Transformation theory of Hamiltonian PDE and the problem
of water waves
. 67
Walter Craig
1
Hamiltonian systems
. 67
2
Partial differential equations as Hamiltonian systems
. 68
3
The problem of water waves
. 71
4
The Dirichlet-Neumann operator
. 73
5
Perturbation theory
. 74
6
The calculus of transformations
. 75
References
. 82
Three theorems on perturbed KdV
. 85
Sergei B. Kuksin
1
KdV equation
. 85
1.1
Integrabilityof(KdV)
. 86
1.2
Normal forms for (KdV)
. 87
2
KAM-theory
. 88
3
Averaging: Hamiltonian perturbations
. 89
4
Averaging: case of non-Hamiltonian perturbations
. 90
4.1
Deterministic perturbations
. 90
4.2
Random perturbations
. 90
References
. 91
Contents xi
Groups and topology in the
Euler
hydrodynamics and KdV
. 93
Boris Khesin
1
Euler
equations and geodesies
. 93
1.1
The
Euler
hydrodynamics equation
. 93
1.2
Geodesies on Lie groups
. 94
1.3
Geodesic description for various equations
. 95
2
Topology of steady flows
. 95
2.1
Arnold's classification of steady fluid flows
. 95
2.2
Variational principles for steady flows
. 97
3
Euler
equations and
integrable
systems
. 98
3.1
Hamiltonian reformulation of the
Euler
equations
. 98
3.2
The Virasoro algebra and the KdV equation
. 99
3.3
Equations-relatives and conservation laws
.100
References
.101
Infinite dimensional dynamical systems and the Navier-Stokes equation
. 103
C. Eugene Wayne
1
First lecture: infinite dimensional dynamical systems
.103
2
Second lecture: invariant manifolds for partial differential
equations on unbounded domains
.
Ill
3
Third lecture: an introduction to the Navier-Stokes equations
. 122
4
Fourth lecture: the long-time asymptotics of solutions
of the two-dimensional Navier-Stokes equation
.129
5
Conclusions
.139
References
.140
Hamiltonian systems and optimal control
. 143
Andrei Agrachev
1
Introduction
.143
2
First lecture
.144
2.1
First order conditions
.145
3
Second lecture
.146
3.1
Second variation
.147
4
Third lecture
.149
4.1
Curves in the
Lagrange Grassmannians.150
4.2
Curvature-type invariants
.151
5
Fourth lecture
.153
References
.156
KAM
theory with applications to Hamiltonian partial
differential equations
.157
Xiaoping Yuan
1
Brief history and basic ideas of
KAM
theory
.157
2
Derivation of the linearized equations
.163
3
Solutions of the linearized equations
.167
4
Applications to partial differential equations
in higher dimensions
.·-----175
xii Contents
Appendix.176
References.
176
Foor
lectures on
KAM
for the non-linear
Schrödinger
equation
.179
L.H. Eliasson and S.B. Kuksin
1
The non-linear
Schrödinger
equation
.179
1.1
The non-linear
Schrödinger
equation
.179
1.2
An «»-dimensional Hamiltonian system
.180
1.3
The topology
.182
1.4
Action-angle variables
.183
1.5
Statement of the result
.184
1.6
KAM-tori
.185
1.7
Consequences of Theorem
1 .186
1.8
References
.188
1.9
Notation
.189
2
The homological equation
.190
2.1
Normal form Hamiltonians
.190
2.2
The KAM-iteration
.191
2.3
The components of the homological equation
.192
2.4
Small divisors and the second Melnikov condition
.194
3
Normal form Hamiltonians
.195
3.1
Blocks
.195
3.2
Lipschitz domains
.197
3.3 Töplitz
at °o(d
= 2).199
3.4 Töplitz-Lipschitz
matrices (d
= 2).200
3.5
Normal form Hamiltonians
.201
4
Estimates of small divisors
.202
4.1
A basic estimate
.202
4.2
The second Melnikov condition (d
= 2).203
5
Functions with the
Töplitz-Lipshitz
property (d
= 2).208
5.1 Töplitz
structure of the Hessian
.208
5.2 Töplitz-Lipschitz
matrices
Jžf x
Jžř
-»
gl(2,R)
.209
5.3
Functions with the
Töplitz-Lipschitz
property
.211
5.4
A short remark on the proof of Theorem
1.1.211
References
.212
A Birkhoff normal form theorem for some
semilinear
PDEs
.213
D.
Bambusi
1
Introduction
.213
2
Birkhoff's theorem in finite dimensions
.214
2.1
Statement
.214
2.2
Proof
.216
3
The case of PDEs
.221
3.1
Hamiltonian formulation of the wave equation
.221
3.2
Extension of Birkhoff's theorem to PDEs:
heuristic ideas
.223
Contents xiii
4
A
Birkhoff normal form
theorem for
semilinear PDEs.224
4.1
Maps with localized coefficients and their properties
. 224
4.2
Statement of the normal form theorem
and its consequences
.228
4.3
Application to the nonlinear wave equation
.229
5
Discussion
.231
6
Proofs
.231
6.1
Proof of the properties of functions with localized
coefficients
.231
6.2
Proof of the Birkhoff normal form Theorem
4.3
and of its dynamical consequences
.236
6.3
Proof of Proposition
4.2
on the verification
of the property of localization of coefficients
.240
6.4
Proof of Theorem
4.4
on the nonresonance condition
. 244
References
.246
Normal form of holomorphic dynamical systems
.249
Laurent Stolovitch
1
Definitions and examples
.249
1.1
Vector fields and differential equations
.250
1.2
Normal forms of vector fields
.253
1.3
Examples about linearization
.256
1.4
Examples about nonlinearizable vector fields
.,258
2
Holomorphic normalization
.259
2.1
Theorem of
A.D.
Brjuno
.259
2.2
Theorems of J. Vey
.261
2.3
Singular complete integrability-Main result
.261
2.4
How to recover Brjuno's and Vey's theorems
from Theorem
2.3.6 .268
2.5
Sketch of the proof
.269
3
Proof of main Theorem
2.3.6.273
3.1
Bounds for the cohomological equations
.273
3.2
Iteration scheme
.277
3.3
Proof of the theorem
.278
4
Miscellaneous results
.280
4.1
Normal forms again
.280
4.2 KAM
theory
.281
4.3
Poisson
structures
.282
References
.283
Geometric approaches to the problem of instability in Hamiltonian
systems. An informal presentation
.285
Amadeu
Delshams, Marian Gidea, Rafael
de la Llave,
and
Tere
M.
Seara
1
Introduction
.285
1.1
Two types of geometric programs
.287
xiv Contents
2 Exposition
of the Arnold example
.289
2.1
The obstruction property
.291
2.2
Some final remarks on the example in [Arn64]
.293
3
Return to a normally hyperbolic manifold. The two dynamics
approach
.294
3.1
The basics of the mechanism of return to a normally
hyperbolic invariant manifold
.294
3.2
The scattering map
.296
3.3
The scattering map and homoclinic intersections
of submanifolds
.298
3.4
Monodramy
of the scattering map
.299
3.5
Smoothness and smooth dependence on parameters
.299
3.6
Geometric properties of the scattering map
.300
3.7
Calculation of the scattering map
.301
4
The large gap model
.303
4.1
Generation of intersections. Melnikov theory
for normally hyperbolic manifolds
.304
4.2
Computation of the scattering map
.307
4.3
The averaging method. Resonant averaging
.308
4.4
Repeated averaging
.312
4.5
Invariant objects generated by resonances: secondary
tori, lower dimensional tori
.312
4.6
Heteroclinic intersections between the invariant objects
generated by resonances
.315
5
The method of correctly aligned windows
.316
6
The large gap model: the method of correctly aligned windows
. 318
7
The large gap model in higher dimensions
.319
8
Instability caused by normally hyperbolic laminations
.320
8.1
Models with two time scales: geodesic flows, billiards
with moving boundaries, Littlewood problems
.321
References
.324
Appendix
.330
Variational methods for the problem of Arnold diffusion
.337
Chong-Qing Cheng
1
Introduction to Mather theory
.337
2
Existence of Homoclinic Orbits
.341
3
Pseudo-COnnecting Orbit Set
"^η,μ,ψ
.342
4
Existence of heteroclinic orbits
.345
5
Construction of global connecting orbits
.353
6
Application to a priori unstable systems
.364
References
.365
Contents xv
The calculus of variations and the forced pendulum
.367
Paul H. Rabinowitz
1
Introduction
.367
2
Periodic solutions
.369
3
Heteroclinic solutions
.374
4
Multitransition solutions: the simplest case
.380
5
Multitransition solutions: general case
.387
6
The tip of the iceberg
.389
References
.390
Variational methods for Hamiltonian PDEs
.391
Massimiliano
Berti
1
Finite dimensions: resonant center theorems
.391
1.1
The variational Lyapunov-Schmidt reduction
.393
2
Infinite dimensions
.396
3
The variational Lyapunov-Schmidt reduction
.397
3.1
The bifurcation equation
.399
4
The small divisor problem
.402
5
The
(öl)-equation .406
6
A variational principle on a Cantor set
.408
7
Forced vibrations
.412
7.1
The variational Lyapunov-Schmidt reduction
.413
7.2
The bifurcation equation
.414
References
.419
Spectral gaps of potentials in weighted Sobolev spaces
.421
Jürgen Pöschel
1
Results
.421
2
Reduction
.425
3
Gap Estimates
.426
4
Coefficient Estimates
.426
5
Modified Weights
.428
References
.429
On the well-posedness of the periodic KdV equation
in high regularity classes
.431
Thomas
Rappeler
and
Jürgen Pöschel
1
Results
.431
2
Birkhoff Coordinates
.435
3
Regularity
.438
References
.440 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| building | Verbundindex |
| bvnumber | BV023356342 |
| classification_rvk | SK 950 |
| ctrlnum | (OCoLC)633880971 (DE-599)DNB986280011 |
| discipline | Maschinenbau / Maschinenwesen Mathematik |
| discipline_str_mv | Maschinenbau / Maschinenwesen Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01705nam a2200421 c 4500</leader><controlfield tag="001">BV023356342</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20080909 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">080623s2008 gw |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">07,N48,0606</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">986280011</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781402069628</subfield><subfield code="c">Gb. : ca. EUR 192.55 (freier Pr.), ca. sfr 313.50 (freier Pr.)</subfield><subfield code="9">978-1-402-06962-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1402069626</subfield><subfield code="c">Gb. : ca. EUR 192.55 (freier Pr.), ca. sfr 313.50 (freier Pr.)</subfield><subfield code="9">1-402-06962-6</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9781402069628</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">11825104</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)633880971</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB986280011</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-BE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">620</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Hamiltonian Dynamical Systems and Applications</subfield><subfield code="c">ed. by Walter Craig</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Springer Netherland</subfield><subfield code="c">2008</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVII, 490 S.</subfield><subfield code="c">235 mm x 155 mm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">NATO Science for Peace and Security Series - B: Physics and Biophysics</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hamiltonsches System</subfield><subfield code="0">(DE-588)4139943-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)1071861417</subfield><subfield code="a">Konferenzschrift</subfield><subfield code="y">2007</subfield><subfield code="z">Montreal</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Hamiltonsches System</subfield><subfield code="0">(DE-588)4139943-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Craig, Walter</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016539877&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016539877</subfield></datafield></record></collection> |
| genre | (DE-588)1071861417 Konferenzschrift 2007 Montreal gnd-content |
| genre_facet | Konferenzschrift 2007 Montreal |
| id | DE-604.BV023356342 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:07:14Z |
| indexdate | 2024-07-09T21:16:43Z |
| institution | BVB |
| isbn | 9781402069628 1402069626 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016539877 |
| oclc_num | 633880971 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XVII, 490 S. 235 mm x 155 mm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer Netherland |
| record_format | marc |
| series2 | NATO Science for Peace and Security Series - B: Physics and Biophysics |
| spelling | Hamiltonian Dynamical Systems and Applications ed. by Walter Craig Dordrecht Springer Netherland 2008 XVII, 490 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier NATO Science for Peace and Security Series - B: Physics and Biophysics Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2007 Montreal gnd-content Hamiltonsches System (DE-588)4139943-2 s DE-604 Craig, Walter Sonstige oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016539877&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hamiltonian Dynamical Systems and Applications Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4139943-2 (DE-588)1071861417 |
| title | Hamiltonian Dynamical Systems and Applications |
| title_auth | Hamiltonian Dynamical Systems and Applications |
| title_exact_search | Hamiltonian Dynamical Systems and Applications |
| title_exact_search_txtP | Hamiltonian Dynamical Systems and Applications |
| title_full | Hamiltonian Dynamical Systems and Applications ed. by Walter Craig |
| title_fullStr | Hamiltonian Dynamical Systems and Applications ed. by Walter Craig |
| title_full_unstemmed | Hamiltonian Dynamical Systems and Applications ed. by Walter Craig |
| title_short | Hamiltonian Dynamical Systems and Applications |
| title_sort | hamiltonian dynamical systems and applications |
| topic | Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Hamiltonsches System Konferenzschrift 2007 Montreal |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016539877&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT craigwalter hamiltoniandynamicalsystemsandapplications |