Regular and chaotic dynamics:
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| Previous Title: | Lieberman, Allan J. Regular ans stochastic motion |
|---|---|
| Main Authors: | , |
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer-Verlag
1992
|
| Edition: | second edition |
| Series: | Applied mathematical sciences
38 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxii, 692 Seiten Illustrationen |
| ISBN: | 0387977457 3540977457 9781441931009 9781475721843 |
Staff View
MARC
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| 100 | 1 | |a Lichtenberg, Allan J. |0 (DE-588)170652246 |4 aut | |
| 245 | 1 | 0 | |a Regular and chaotic dynamics |c A. J. Lichtenberg ; M. A. Lieberman |
| 250 | |a second edition | ||
| 264 | 1 | |a New York |b Springer-Verlag |c 1992 | |
| 300 | |a xxii, 692 Seiten |b Illustrationen | ||
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| 650 | 0 | 7 | |a Nichtlineares dynamisches System |0 (DE-588)4126142-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastische Strömung |0 (DE-588)4195753-2 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804119747777789952 |
|---|---|
| adam_text | Contents
Preface
Preface to the First Edition
List of Symbols
chapter
Overview and Basic Concepts
1.1.
*1.2. Transformation Theory of Mechanics
*1.2a. Canonical Transformations
*1.2b. Motion in Phase Space
*1.2c. Action-Angle Variables
1.3.
»1.3a. One Degree of Freedom
1.3b. Linear Differential Equations
1.3c. More than One Degree of Freedom
1.3d. Noncanonical Variables and Reduction
*1.4. Near-Integrable Systems
*
»1.4b. More than Two Degrees of Freedom
1.5.
1.5a. Strange Attractors
1.5b. The
CHAPTER
Canonical Perturbation Theory
2.1.
2.1a. Power Series
2.1b. Asymptotic Series and Small Denominators
2.1c. The Effect of Resonances
*2.2. Classical Perturbation Theory
*2.2a. One Degree of Freedom
*2.2b. Two or More Degrees of Freedom
xii Contents
2.3.
*2.3a. Introduction and Basic Concepts
*2.3b. Canonical Adiabatic
*2.3c.
2.3d. Noncanonical Methods
2.4.
*2.4a. Removal of Resonances
*2.4b. Higher-Order Resonances
*2.4c. Resonant Wave-Particle Interaction
2.4d. Global Removal of Resonances
2.5.
2.5a. General Theory
2.5b. Deprit Perturbation Series
2.5c. Adiabatic Invariants
2.6.
2.6a. Kolmogorov s Technique
2.6b. Singly Periodic Orbits
CHAPTER
Mappings and Linear Stability
*3.1. Hamiltonian Systems as Canonical Mappings
*3.1a.
*3.1b. Near-Integrable Systems
*3.1c. Hamiltonian Forms and Mappings
*3.2. Generic Behavior of Canonical Mappings
*3.2a. Irrational Winding Numbers and
*3.2b. Rational Winding Numbers and Their Structure
*3.2c. Complete Description of a Nonlinear Mapping
*3.2d. Numerical Examples
3.3.
*3.3a. Eigenvalues and Eigenvectors of a Matrix
*3.3b. Two-Dimensional Mappings
3.3c. Linear Stability in Higher Dimensions
3.3d. General Stability Concepts
*3.4. Mapping Models
*3.4a. Physical Problems and Models
*3.4b. Numerical Results
*3.4c. Fixed Points and Linear Stability
*3.4d. Bifurcation Phenomena
*3.4e. Hamiltonian Formulation
*3.5. The Separatrix Motion
*3.5a. Driven One-Dimensional Pendulum
*3.5b. The Separatrix Mapping
3.6.
3.6a. Tiling of the Phase Space
3.6b. Phase Space Structure
Contents xiii
CHAPTER
Transition to Global Stochasticity
*4.1. Introduction
*4.1a. Qualitative Description of Criteria
*4.1b. The Standard Mapping
*4.2. Resonance Overlap
*4.2a. Rationale for Criteria
*4.2b. Calculation of Overlap Criteria
4.3.
4.3a. Elliptic Fixed Points
4.3b. The Separatrix
*4.4. Stability of High-Order Fixed Points
*4.4a. The Basic Elements of Greene s Method
*4.4b. Numerical Evaluation
4.5.
4.6.
*4.7. Summary and Conclusions
CHAPTER
Stochastic Motion and Diffusion
5.1.
5.2.
*5.2a. Ergodicity
*5.2b. Liapunov Characteristic Exponents
5.2c. Concepts of Stochasticity
5.2d. Randomness and Numerical Errors
5.3.
5.3a. Analytical Estimates
*5.3b. Numerical Methods
*5.4. Diffusion in Action Space
*5.4a. The Fokker-Planck Equation
*5.4b. Transport Coefficients
*5.4c. Steady-State and Transient Solutions
5.5.
5.5a. Higher-Order Transport Corrections
5.5b. Diffusion near Critical
5.5c.
5.5d. Quasiaccelerator Modes
5.6.
5.6a. Introduction
5.6b. Diffusion in the Presence of Resonances
5.6c. Diffusion on Two Space and Time Scales
5.7.
xiv Contents
CHAPTER
Three or More Degrees of Freedom
♦б.і.
*6.1a. Geometric Relations
*6.1b. Examples of Arnold Diffusion
6.2.
♦6.2a. Stochastic Pump Diffusion Calculation
6.2b. Coupling Resonance Diffusion
6.2c. Many Resonance Diffusion
6.2d. Modulational Diffusion
6.3.
6.3a. Resonance Streaming
6.3b. Diffusion of a Parameter
6.4.
6.4a. Magnetic Islands
6.4b. Drift Surfaces and Diffusion in Static Fields
6.4c. Time-Varying Fields
6.4d. The Self-Consistent Problem
6.5.
6.5a. Strongly Nonlinear Coupled Systems
6.5b. The Fermi-Pasta-Ulam Model and the
Korteveg-de
6.5c. Discretized Sine-Gordon Equation
CHAPTER
Bifurcation Phenomena and Transition
to Chaos in Dissipative Systems
7.1.
7.1a. Basic Properties
7.1b. Simple Attractors and Their Bifurcations
7.1c. Examples of Strange Attractors
7.
7.2.
7.2a. Basic Properties
7.2b. Periodic Behavior
7.2c. Chaotic Motion
7.3.
7.3a. Dissipative Maps
7.3b. Area-Preserving Maps
7.3c. Transition Between Hamiltonian and Dissipative Chaos
7.4.
7.4a. Basic Formalism
7.4b. Critical Behavior and Universality
7.4c. Supercritical Behavior
7.4d. Physical Examples
7.5.
7.5a. Intermittency Mechanisms
7.5b. Renormalization-Group Analysis
Contents xv
7.5c. Power
7.6.
7.6a. Crises
7.6b. Fractal Basin Boundaries
7.7.
CHAPTER
Chaotic Motion in Dissipative Systems
8.1.
8.1a. Weak Dissipation
8.1b. Transient Chaos Near a Crisis
8.2.
8.2a. Reduction to a One-Dimensional Map
8.2b. Direct Iteration of an Initial Distribution
8.3.
8.3a. Generalized Dimensions
8.3b. Scaling Index Spectrum
8.4.
8.4a. Delay Coordinates and Embedding Dimension
8.4b. Statistical Quantities
8.4c. Short-Time Prediction
8.5.
8.5a. Maps on a Lattice
8.5b. Self-Organized Criticality
8.6.
8.6a. Fourier Mode Expansions
8.6b. The Transition to Turbulence
8.6c. Hamiltonian Chaos in Fluids
APPENDIX A
Applications
АЛ.
A.2. Accelerators and Beams
A3.
A.4. Charged Particle Heating
A.5. Chemical Dynamics
A.6. Quantum Systems
Bibliography
Author Index
Subject Index
|
| any_adam_object | 1 |
| author | Lichtenberg, Allan J. Lieberman, Michael A. 1940- |
| author_GND | (DE-588)170652246 (DE-588)1139215000 |
| author_facet | Lichtenberg, Allan J. Lieberman, Michael A. 1940- |
| author_role | aut aut |
| author_sort | Lichtenberg, Allan J. |
| author_variant | a j l aj ajl m a l ma mal |
| building | Verbundindex |
| bvnumber | BV005527514 |
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| classification_tum | MAT 605f MAT 587f MAT 584f MAT 344f |
| ctrlnum | (OCoLC)246686541 (DE-599)BVBBV005527514 |
| discipline | Physik Mathematik |
| edition | second edition |
| format | Book |
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| id | DE-604.BV005527514 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:31:07Z |
| institution | BVB |
| isbn | 0387977457 3540977457 9781441931009 9781475721843 |
| language | English |
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| publishDate | 1992 |
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| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Lichtenberg, Allan J. (DE-588)170652246 aut Regular and chaotic dynamics A. J. Lichtenberg ; M. A. Lieberman second edition New York Springer-Verlag 1992 xxii, 692 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 38 Chaotisches System (DE-588)4316104-2 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Stochastische Strömung (DE-588)4195753-2 gnd rswk-swf Chaotisches System (DE-588)4316104-2 s Nichtlineares dynamisches System (DE-588)4126142-2 s DE-604 Stochastische Strömung (DE-588)4195753-2 s Lieberman, Michael A. 1940- (DE-588)1139215000 aut Erscheint auch als Online-Ausgabe 978-1-4757-2184-3 1. Auflage Lieberman, Allan J. Regular ans stochastic motion (DE-604)BV000231046 Applied mathematical sciences 38 (DE-604)BV000005274 38 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003463885&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lichtenberg, Allan J. Lieberman, Michael A. 1940- Regular and chaotic dynamics Applied mathematical sciences Chaotisches System (DE-588)4316104-2 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Stochastische Strömung (DE-588)4195753-2 gnd |
| subject_GND | (DE-588)4316104-2 (DE-588)4126142-2 (DE-588)4195753-2 |
| title | Regular and chaotic dynamics |
| title_auth | Regular and chaotic dynamics |
| title_exact_search | Regular and chaotic dynamics |
| title_full | Regular and chaotic dynamics A. J. Lichtenberg ; M. A. Lieberman |
| title_fullStr | Regular and chaotic dynamics A. J. Lichtenberg ; M. A. Lieberman |
| title_full_unstemmed | Regular and chaotic dynamics A. J. Lichtenberg ; M. A. Lieberman |
| title_old | Lieberman, Allan J. Regular ans stochastic motion |
| title_short | Regular and chaotic dynamics |
| title_sort | regular and chaotic dynamics |
| topic | Chaotisches System (DE-588)4316104-2 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Stochastische Strömung (DE-588)4195753-2 gnd |
| topic_facet | Chaotisches System Nichtlineares dynamisches System Stochastische Strömung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003463885&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT lichtenbergallanj regularandchaoticdynamics AT liebermanmichaela regularandchaoticdynamics |