Hamiltonian chaos and fractional dynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2006
|
| Ausgabe: | Reprinted |
| Schlagworte: | |
| Online-Zugang: | Table of contents Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIV, 421 S. Ill., graph. Darst. |
| ISBN: | 0198526040 |
Internformat
MARC
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| 100 | 1 | |a Zaslavsky, George M. |d 1935-2008 |e Verfasser |0 (DE-588)13657985X |4 aut | |
| 245 | 1 | 0 | |a Hamiltonian chaos and fractional dynamics |c George M. Zaslavsky |
| 250 | |a Reprinted | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2006 | |
| 300 | |a XIV, 421 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a aHamiltonian systems | |
| 650 | 4 | |a aChaotic behavior in systems | |
| 650 | 0 | 7 | |a Hamilton-Formalismus |0 (DE-588)4376155-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineares dynamisches System |0 (DE-588)4126142-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Chaotisches System |0 (DE-588)4316104-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hamiltonsches System |0 (DE-588)4139943-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineares dynamisches System |0 (DE-588)4126142-2 |D s |
| 689 | 0 | 1 | |a Hamiltonsches System |0 (DE-588)4139943-2 |D s |
| 689 | 0 | 2 | |a Chaotisches System |0 (DE-588)4316104-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Hamilton-Formalismus |0 (DE-588)4376155-0 |D s |
| 689 | 1 | 1 | |a Chaotisches System |0 (DE-588)4316104-2 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 856 | 4 | |u http://www.loc.gov/catdir/toc/ecip0421/2004018403.html |3 Table of contents | |
| 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=013083272&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-013083272 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804133230931083264 |
|---|---|
| adam_text | CONTENTS
Part
1
Chaotic Dynamics
1
Hamiltonian dynamics
3
1.1
Hamiltonian equations
3
1.2
Phase space dynamics
5
1.3
Action-angle variable (one degree of freedom)
8
Notes
Problems
2
Examples of Hamiltonian dynamics
13
2.1
Pendulum
13
2.2
Oscillations in the infinite potential well
16
2.3
Magnetic moments
17
2.4
Field line behaviour
18
2.5
Hamiltonian equations for the ABC-flow
20
Problems
22
3
Perturbed dynamics
23
3.1
The Liouville-Arnold theorem on integrability
23
3.2
Consequences of the integrability
25
3.3
Non-integrability and the Kozlov condition
26
3.4
Resonances
28
3.5
Non-linear resonance and chain of islands
29
3.6
Kolmogorov-Arnold-Moser
(KAM)
theory
32
Notes
Problems
4
Chaotic dynamics
37
4.1
Natural measure
37
4.2
Ergodicity, mixing, and weak mixing
39
4.3
Local instability and
Lýapunov
exponents
42
4.4
Hyperbolic systems
46
4.5
Entropy of dynamical systems
48
4.5.1
Partitioning and coarse-graining
48
4.5.2
Kolmogorov-Smai (KS) entropy
49
4.5.3
Topological entropy
51
4.5.4
Physical interpretation
51
4.5.5
Entropy and Lyapunov exponents
53
CONTENTS
4.6 Definition
of chaotic dynamics
53
4.7
Chirikov resonance overlapping criteria
54
Notes
Problems
Physical models of chaos
57
5.1
Mapping the dynamics
57
5.2
Universal and standard map
60
5.3
Web map (kicked oscillator)
64
5.4
Kepler map
68
Notes
Problems
Separatrix chaos
73
6.1
Description of models
73
6.2
Separatrix map
76
6.3
The stochastic layer
78
6.4
The stochastic layer of the standard map
81
6.5
Hidden renormalization group near
the separatrix
83
6.6
Renormalization of resonances
89
6.7
Hidden renormalization for coupled oscillators
91
Notes
Problems
Weak chaos and symmetry
97
7.1
Stochastic webs
97
7.2
Stochastic webs with quasi-crystalline symmetry
99
7.3
Stochastic web skeleton
102
7.4
Symmetries and their dynamical generation
110
7.5
Width of the stochastic web
114
7.6
Symmetry in art and nature
117
7.6.1
Symmetry and chaos
117
7.6.2
Ornamental patterns
118
7.6.3
Patterns in nature
120
Notes
Problems
Beyond the KAM-theory
125
8.1
Small non-linearity
125
8.2
Web-Tori
127
8.3
Width of the stochastic web
134
8.4
Transition from KAM-Tori to Web-Tori
135
Notes
Problems
CONTENTS
9 Phase
space of
chaos
139
9.1
Topological non-
universality of
chaos
139
9.2
Examples with billiards
142
9.3
Accelerator mode islands
143
9.4
Ballistic mode islands
151
9.5
Cantori
152
9.6
Sticky domains and escapes
154
Notes
Problems
Part
2
Practality of Chaos
10
Fractals and chaos
159
10.1
Fractal dynamics
159
10.2
Generalized fractal dimension
161
10.3
Renormalization group and generalized fractal
dimension
162
10.4
Multifractal spectra
164
10.5
Thermodynamic interpretation
167
10.6
Complex dimension and log-periodicity
169
Notes
Problems
11
Poincaré
recurrences
173
11.1
Poincaré
theorem on recurrences
173
11.2
Recurrence time distributions and
Кас
lemma
174
11.3
Distribution of recurrences in uniform mixing
177
11.4
More asymptotics on recurrences
180
Notes
Problems
12
Dynamical traps
187
12.1
Definition of the dynamical trap
187
12.2
Hierarchical-islands trap (HIT)
189
12.3
Renormalization for the exit time distribution
193
12.4
Stochastic layer trap
196
Notes
13
Fractal time
201
13.1
Fractal time
201
13.2
Fractal and multifractal recurrences
204
13.3
Multifractal space-time and its dimension spectrum
207
13.4
Critical exponent for the
Poincaré
recurrences
209
Notes
Problems
CONTENTS
Part
3
Chaotic kinetics
14
General principles of kinetics
215
14.1
Time scales
215
14.2
Fokker-Planck-Kolmogorov
(FPK)
equation
217
14.3
Detailed balance principle
220
14.4
Solutions and normal transport
221
14.5
Growth of entropy
222
14.6
Kolmogorov conditions and conflict with dynamics
223
14.7
Truncated distributions
225
Notes
Problems
15
Levy process, Levy flights, and
Weierstrass
random walk
229
15.1
Levy distribution
230
15.2
Levy process
231
15.3
Poincaré
recurrences and Feller s theorems
234
15.4
Levy flights and conflict with dynamics
235
15.5
Weirstrass random walks (WRW)
240
Notes
Problems
16
Fractional kinetic equation (FKE)
245
16.1
Derivation of FKE
245
16.2
Conditions for the FKE
249
16.3
Evolution of moments (transport)
250
16.4
Conflict with dynamics
252
16.5
Dynamical origin of critical exponents
253
16.6
Principles of simulations
257
Notes
Problems
17
Renormalization group of kinetics (RGK)
261
17.1
Space-time scalings
261
17.2
Log-periodicity
263
17.3
Duality of the dynamics and the origin of multi-fractality
265
17.4
Multifractional kinetics
267
Notes
18
Fractional kinetic equation: solutions and modifications
273
18.1
Solutions to FKE (series)
273
18.2
Solutions to FKE (separation of variables)
275
18.3
Continuous time random walk (CTRW)
276
18.4
Levy walks and other generalizations of CTRW
279
18.5
Conflict with dynamics
281
18.6
Subdiffusion
and
superdiffusion
281
CONTENTS
Notes
Problems
19
Pseudochaos
287
19.1
Billiards in polygons
287
19.2
Continued fractions and scalings of trajectories
291
19.3
Fractional kinetics of irrational trajectories
296
19.4
More examples of
pseudochaos
303
19.4.1
Rhombic billiard
303
19.4.2
More billiards
303
19.4.3
Saw-tooth web map
306
Notes
Problems
Part
4
Applications
20
Complexity and entropy of dynamics
315
20.1
Complexity in phase space
316
20.2
Symbolic and topological complexities
317
20.3
Topological and metric entropies
320
20.4
Conflict with dynamics
323
Notes
Problems
21
Complexity and entropy functions
325
21.1
Definitions of complexity function
325
21.2
Probability of e-divergence
328
21.3
Calculation of local complexity function
329
21.4
Flight complexity function
331
21.5
Entropy function
333
21.6
Polynomial and mixed complexities and anomalous transport
335
21.7
Travelling waves and Riemann invariants of entropy and
complexity
337
Notes
Problems
22
Chaos and foundation of statistical
mechanics
341
22.1
Zermelo s and Loschmidt s paradoxes
341
22.1.1
Historical comments
341
22.1.2
Paradox of recurrence
342
22.1.3
Paradox of reversibility
343
22.1.4
Boltzmann s comments
343
22.2
Chaos and the paradoxes
344
22.3
Anomalous properties of the Sinai and Bunimovich billiards
344
22.4
Maxwell s Demon and Chaos
346
CONTENTS
22.5
Maxwell s Demon as a dynamical model
348
22.6
Comments on the application of Ergodic Theory
352
22.7
Comments on dynamical cooling and chaos erasing
352
Notes
23
Chaotic advection (dynamics of tracers)
357
23.1
Beltrami flows with g-symmetry
357
23.2
Compressible helical flows
359
23.3
Compressible flow with quasi-symmetry
367
Notes
Problems
24
Advection by point vortices
373
24.1
Basic equations for point vortices and for advection
373
24.2
Advection in three vortices
376
24.3
Transport of advected particles (vortices)
383
Notes
Problems
Appendices
393
A Elliptic integrals and elliptic functions
393
В
Spectrum of the Kepler problem
394
С
Fractional integro-diferentiation
396
D
Formulas of fractional calculus
399
References
403
Index
417
|
| any_adam_object | 1 |
| author | Zaslavsky, George M. 1935-2008 |
| author_GND | (DE-588)13657985X |
| author_facet | Zaslavsky, George M. 1935-2008 |
| author_role | aut |
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| ctrlnum | (OCoLC)255571210 (DE-599)BVBBV019756825 |
| dewey-full | 530.15474 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15474 |
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| dewey-sort | 3530.15474 |
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| discipline | Physik Mathematik |
| edition | Reprinted |
| format | Book |
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| id | DE-604.BV019756825 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:05:25Z |
| institution | BVB |
| isbn | 0198526040 |
| language | English |
| lccn | 2004018403 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013083272 |
| oclc_num | 255571210 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR |
| owner_facet | DE-703 DE-355 DE-BY-UBR |
| physical | XIV, 421 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Zaslavsky, George M. 1935-2008 Verfasser (DE-588)13657985X aut Hamiltonian chaos and fractional dynamics George M. Zaslavsky Reprinted Oxford [u.a.] Oxford Univ. Press 2006 XIV, 421 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index aHamiltonian systems aChaotic behavior in systems Hamilton-Formalismus (DE-588)4376155-0 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 s Hamiltonsches System (DE-588)4139943-2 s Chaotisches System (DE-588)4316104-2 s DE-604 Hamilton-Formalismus (DE-588)4376155-0 s 1\p DE-604 http://www.loc.gov/catdir/toc/ecip0421/2004018403.html Table of contents Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013083272&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Zaslavsky, George M. 1935-2008 Hamiltonian chaos and fractional dynamics aHamiltonian systems aChaotic behavior in systems Hamilton-Formalismus (DE-588)4376155-0 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Chaotisches System (DE-588)4316104-2 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4376155-0 (DE-588)4126142-2 (DE-588)4316104-2 (DE-588)4139943-2 |
| title | Hamiltonian chaos and fractional dynamics |
| title_auth | Hamiltonian chaos and fractional dynamics |
| title_exact_search | Hamiltonian chaos and fractional dynamics |
| title_full | Hamiltonian chaos and fractional dynamics George M. Zaslavsky |
| title_fullStr | Hamiltonian chaos and fractional dynamics George M. Zaslavsky |
| title_full_unstemmed | Hamiltonian chaos and fractional dynamics George M. Zaslavsky |
| title_short | Hamiltonian chaos and fractional dynamics |
| title_sort | hamiltonian chaos and fractional dynamics |
| topic | aHamiltonian systems aChaotic behavior in systems Hamilton-Formalismus (DE-588)4376155-0 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Chaotisches System (DE-588)4316104-2 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | aHamiltonian systems aChaotic behavior in systems Hamilton-Formalismus Nichtlineares dynamisches System Chaotisches System Hamiltonsches System |
| url | http://www.loc.gov/catdir/toc/ecip0421/2004018403.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013083272&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT zaslavskygeorgem hamiltonianchaosandfractionaldynamics |