High-dimensional chaotic and attractor systems: a comprehensive introduction
Gespeichert in:
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| Sprache: | English |
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Dordrecht
Springer
2007
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| Schriftenreihe: | Intelligent systems, control and automation: science and engineering
32 |
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| Beschreibung: | XVI, 700 S. |
| ISBN: | 9781402054556 |
Internformat
MARC
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| 020 | |a 9781402054556 |c Gb. : EUR 139.05 (freier Pr.), sfr 220.00 (freier Pr.) |9 978-1-4020-5455-6 | ||
| 035 | |a (OCoLC)77077731 | ||
| 035 | |a (DE-599)BVBBV022933492 | ||
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| 084 | |a 530 |2 sdnb | ||
| 100 | 1 | |a Ivancevic, Vladimir G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a High-dimensional chaotic and attractor systems |b a comprehensive introduction |c Vladimir G. Ivancevic ; Tijana T. Ivancevic |
| 264 | 1 | |a Dordrecht |b Springer |c 2007 | |
| 300 | |a XVI, 700 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Intelligent systems, control and automation: science and engineering |v 32 | |
| 650 | 7 | |a Atratores |2 larpcal | |
| 650 | 7 | |a Caos (sistemas dinâmicos) |2 larpcal | |
| 650 | 4 | |a Dynamics | |
| 650 | 4 | |a Mechanics, Analytic | |
| 650 | 0 | 7 | |a Attraktor |0 (DE-588)4140563-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hochdimensionales System |0 (DE-588)4202326-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Chaotisches System |0 (DE-588)4316104-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Chaotisches System |0 (DE-588)4316104-2 |D s |
| 689 | 0 | 1 | |a Attraktor |0 (DE-588)4140563-8 |D s |
| 689 | 0 | 2 | |a Hochdimensionales System |0 (DE-588)4202326-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Ivancevic, Tijana T. |e Verfasser |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4020-5456-3 |
| 830 | 0 | |a Intelligent systems, control and automation: science and engineering |v 32 |w (DE-604)BV024977557 |9 32 | |
| 856 | 4 | 2 | |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=2844159&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016138282&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016138282 | |
Datensatz im Suchindex
| _version_ | 1805089543282491392 |
|---|---|
| adam_text |
Contents
Preface
.xiii
Acknowledgments
. xv
1
Introduction to Attractors and Chaos
. 1
1.1
Basics of Attractor and Chaotic Dynamics
. 17
1.2
A Brief History of Chaos Theory in
5
Steps
. 29
1.2.1
Henry
Poincaré:
Qualitative Dynamics, Topology- and
Chaos
. 30
1.2.2
Stephen
Smale: Topological
Horseshoe and Chaos of
Stretching and Folding
. 38
1.2.3
Ed
Lorenz:
Weather Prediction and Chaos
. 48
1.2.4
Mitchell
Feigenbaum:
A Constant and Universality
. 51
1.2.5
Lord Robert May: Population Modelling and Chaos
. 52
1.2.6
Michel
Hénon:
A Special 2D Map and Its Strange
Attractor
. 56
1.3
Some Classical Attractor and Chaotic Systems
. 59
1.4
Basics of Continuous Dynamical Analysis
. 72
1.4.1
A Motivating Example
. 72
1.4.2
Systems of ODEs
. 75
1.4.3
Linear Autonomous Dynamics: Attractors
&
Repellors
. 78
1.4.4
Conservative versus Dissipative Dynamics
. 82
1.4.5
Basics of Nonlinear Dynamics
. 89
1.4.6
Ergodic Systems
.108
1.5
Continuous Chaotic Dynamics
.109
1.5.1
Dynamics and Non-Equilibrium Statistical Mechanics.
.111
1.5.2
Statistical Mechanics of Nonlinear Oscillator Chains
. . . 124
1.5.3
Geometrical Modelling of Continuous Dynamics
.125
1.5.4
Lagrangian Chaos
.128
1.6
Standard Map and Hamiltonian Chaos
.136
1.7
Chaotic Dynamics of Binary Systems
.142
1.7.1
Examples of Dynamical Maps
.144
1.7.2
Correlation Dimension of an Attractor
.148
1.8
Basic Hamiltonian Model of
Biodynamics
.149
vii
Contents
Smale
Horseshoes and Homoclinic Dynamics
.153
2.1
Smale
Horseshoe Orbits and Symbolic Dynamics
.153
2.1.1
Horseshoe Trellis
.157
2.1.2
Trellis-Forced Dynamics
.161
2.1.3
Homoclinic Braid Type
.164
2.2
Homoclinic Classes for Generic Vector-Fields
.165
2.2.1
Lyapunov Stability
.168
2.2.2
Homoclinic Classes
.171
2.3
Complex-Valued
Hénon
Maps and Horseshoes
.174
2.3.1
Complex Henon-Like Maps
.175
2.3.2
Complex Horseshoes
.178
2.4
Chaos in Functional Delay Equations
.181
2.4.1
Poincaré
Maps and Homoclinic Solutions
.184
2.4.2
Starting Value and Targets
.192
2.4.3
Successive Modifications of
g
.199
2.4.4
Transversality
.215
2.4.5
Transversally Homoclinic Solutions
.221
3-Body Problem and Chaos Control
.223
3.1
Mechanical Origin of Chaos
.223
3.1.1
Restricted 3-Body Problem
.224
3.1.2
Scaling and Reduction in the 3-Body Problem
.236
3.1.3
Periodic Solutions of the 3-Body Problem
.239
3.1.4
Bifurcating Periodic Solutions of the 3-Body Problem.
. 240
3.1.5
Bifurcations in Lagrangian Equilibria
.241
3.1.6
Continuation of KAM-Tori
.247
3.1.7
Parametric Resonance and Chaos in Cosmology
.249
3.2
Elements of Chaos Control
.252
3.2.1
Feedback and Non-Feedback Algorithms for Chaos
Control
.252
3.2.2
Exploiting Critical Sensitivity
.256
3.2.3
Lyapunov Exponents and Kaplan-Yorke Dimension
. 257
3.2.4
Kolmogorov-Sinai Entropy
.259
3.2.5
Chaos Control by
Ott,
Grebogi and Yorke (OGY)
.261
3.2.6
Floquet Stability Analysis and OGY Control
.264
3.2.7
Blind Chaos Control
.268
3.2.8
Jerk Functions of Simple Chaotic Flows
.272
3.2.9
Example: Chaos Control in Molecular Dynamics
.275
Phase Transitions and Synergetics
.285
4.1
Phase Transitions, Partition Function and Noise
.285
4.1.1
Equilibrium Phase Transitions
.285
4.1.2
Classification of Phase Transitions
.286
4.1.3
Basic Properties of Phase Transitions
.288
4.1.4
Landau's Theory of Phase Transitions
.290
Contents ix
4.1.5 Partition
Function
.292
4.1.6
Noise-Induced Non-equilibrium Phase Transitions
.299
4.2
Elements of Haken's Synergetics
.306
4.2.1
Phase Transitions
.308
4.2.2
Mezoscopic Derivation of Order Parameters
.310
4.2.3
Example: Synergetic Control of
Biodynamics
.312
4.2.4
Example: Chaotic Psychodynamics of Perception
.313
4.2.5
Kick Dynamics and Dissipation-Fluctuation Theorem
. . 317
4.3
Synergetics of Recurrent and Attractor Neural Networks
.320
4.3.1
Stochastic Dynamics of
Neuronal
Firing States
.322
4.3.2
Synaptic Symmetry and Lyapunov Functions
.327
4.3.3
Detailed Balance and Equilibrium Statistical Mechanics
329
4.3.4
Simple Recurrent Networks with Binary Neurons
.334
4.3.5
Simple Recurrent Networks of Coupled Oscillators
.343
4.3.6
Attractor Neural Networks with Binary Neurons
.350
4.3.7
Attractor Neural Networks with Continuous Neurons
. . 362
4.3.8
Correlation- and Response-Functions
.369
4.3.9
Path-Integral Approach for Complex Dynamics
.378
4.3.10
Hierarchical Self-Programming in Neural Networks
. 399
4.4
Topological Phase Transitions and Hamiltonian Chaos
.406
4.4.1
Phase Transitions in Hamiltonian Systems
.406
4.4.2
Geometry of the Largest Lyapunov Exponent
.408
4.4.3
Euler
Characteristics of Hamiltonian Systems
.412
4.4.4
Pathways to Self-Organization in Human
Biodynamics
. 416
Phase Synchronization in Chaotic Systems
.419
5.1
Lyapunov Vectors and Lyapunov Exponents
.419
5.1.1
Forced
Rössler
Oscillator
.422
5.1.2
Second Lyapunov Exponent: Perturbative Calculation.
. 424
5.2
Phase Synchronization in Coupled Chaotic Oscillators
.426
5.3
Oscillatory Phase
Neurodynamics
.430
5.3.1
Kuramoto Synchronization Model
.432
5.3.2
Lyapunov Chaotic Synchronization
.433
5.4
Synchronization Geometry
.435
5.4.1
Geometry of Coupled Nonlinear Oscillators
.435
5.4.2
Noisy Coupled Nonlinear Oscillators
.439
5.4.3
Synchronization Condition
.448
5.5
Complex Networks and Chaotic Transients
.451
Josephson
Junctions and Quantum Engineering
.457
6.0.1
Josephson
Effect
.460
6.0.2
Pendulum Analog
.461
6.1
Dissipative
Josephson
Junction
.463
6.1.1
Junction Hamiltonian and its Eigenstates
.464
6.1.2
Transition Rate
.466
χ
Contents
6.2
Josephson
Junction Ladder (JJL)
.467
6.2.1
Underdamped JJL
.473
6.3
Synchronization in Arrays of
Josephson
Junctions
.477
6.3.1
Phase Model for Underdamped JJL
.479
6.3.2
Comparison of LKM2 and RCSJ Models
.485
6.3.3
'Small-World' Connections in JJL Arrays
.486
7
Fractals and Fractional Dynamics
.491
7.1
Fractals
.491
7.1.1
Mandelbrot Set
.491
7.2
Robust Strange Non-Chaotic Attractors
.494
7.2.1
Quasi-Periodically Forced Maps
.494
7.2.2
2D Map on a Torus
.497
7.2.3
High Dimensional Maps
.502
7.3
Effective Dynamics in Hamiltonian Systems
.505
7.3.1
Effective Dynamical Invariants
.507
7.4
Formation of Fractal Structure in Many-Body Systems
.508
7.4.1
A Many-Body Hamiltonian
.509
7.4.2
Linear Perturbation Analysis
.509
7.5
Fractional Calculus and Chaos Control
.512
7.5.1
Fractional Calculus
.512
7.5.2
Fractional-Order Chua's Circuit
.514
7.5.3
Feedback Control of Chaos
.515
7.6
Fractional Gradient and Hamiltonian Dynamics
.516
7.6.1
Gradient Systems
.517
7.6.2
Fractional Differential Forms
.518
7.6.3
Fractional Gradient Systems
.519
7.6.4
Hamiltonian Systems
.523
7.6.5
Fractional Hamiltonian Systems
.524
8
Turbulence
.529
8.1
Parameter-Space Analysis of the
Lorenz Attractor.529
8.1.1
Structure of the Parameter-Space
.531
8.1.2
Attractors and Bifurcations
.538
8.2
Periodically-Driven
Lorenz
Dynamics
.539
8.2.1
Toy Model Illustration
.542
8.3 Lorenzian
Diffusion
.545
8.4
Turbulence
.549
8.4.1
Turbulent Flow
.550
8.4.2
The Governing Equations of Turbulence
.552
8.4.3
Global Well-Posedness of the Navier-Stokes Equations
. 553
8.4.4
Spatio-Temporal
Chaos and Turbulence in PDEs
.554
8.4.5
General Fluid Dynamics
.559
8.4.6
Computational Fluid Dynamics
.563
8.5
Turbulence Kinetics
.565
Contents xi
8.5.1
Kinetic Theory
.567
8.5.2
Filtered Kinetic Theory
.570
8.5.3
Hydrodynamic Limit
.572
8.5.4
Hydrodynamic Equations
.574
8.6
Lie Symmetries in the Models of Turbulence
.575
8.6.1
Lie Symmetries and Prolongations on Manifolds
.576
8.6.2
Noether Theorem and Navier-Stokes Equations
.589
8.6.3
Large-Eddy Simulation
.591
8.6.4
Model Analysis
.594
8.6.5
Thermodynamic Consistence
.600
8.6.6
Stability of Turbulence Models
.602
8.7
Advection of Vector-Fields by Chaotic Flows
.603
8.7.1
Advective Fluid Flow
.603
8.7.2
Chaotic Flows
.606
8.8
Brownian Motion and Diffusion
.607
8.8.1
Random Walk Model
.607
8.8.2
More Complicated Transport Processes
.609
8.8.3
Advection-Diffusion
.609
8.8.4
Beyond the Diffusion Coefficient
.614
9
Geometry,
Solitons
and Chaos Field Theory
.617
9.1
Chaotic Dynamics and Riemannian Geometry
.617
9.2
Chaos in Physical Gauge Fields
.620
9.3
Solitions
.625
9.3.1
History of
Solitons in
Brief
.625
9.3.2
The Fermi-Pasta-Ulam Experiments
.630
9.3.3
The Kruskal-Zabusky Experiments
.635
9.3.4
A First Look at the KdV Equation
.638
9.3.5
Split-Stepping KdV
.641
9.3.6 Solitons
from a Pendulum Chain
.643
9.3.7
ID Crystal Soliton
.644
9.3.8 Solitons
and Chaotic Systems
.645
9.4
Chaos Field Theory
.649
References
.653
Index
.689 |
| adam_txt |
Contents
Preface
.xiii
Acknowledgments
. xv
1
Introduction to Attractors and Chaos
. 1
1.1
Basics of Attractor and Chaotic Dynamics
. 17
1.2
A Brief History of Chaos Theory in
5
Steps
. 29
1.2.1
Henry
Poincaré:
Qualitative Dynamics, Topology- and
Chaos
. 30
1.2.2
Stephen
Smale: Topological
Horseshoe and Chaos of
Stretching and Folding
. 38
1.2.3
Ed
Lorenz:
Weather Prediction and Chaos
. 48
1.2.4
Mitchell
Feigenbaum:
A Constant and Universality
. 51
1.2.5
Lord Robert May: Population Modelling and Chaos
. 52
1.2.6
Michel
Hénon:
A Special 2D Map and Its Strange
Attractor
. 56
1.3
Some Classical Attractor and Chaotic Systems
. 59
1.4
Basics of Continuous Dynamical Analysis
. 72
1.4.1
A Motivating Example
. 72
1.4.2
Systems of ODEs
. 75
1.4.3
Linear Autonomous Dynamics: Attractors
&
Repellors
. 78
1.4.4
Conservative versus Dissipative Dynamics
. 82
1.4.5
Basics of Nonlinear Dynamics
. 89
1.4.6
Ergodic Systems
.108
1.5
Continuous Chaotic Dynamics
.109
1.5.1
Dynamics and Non-Equilibrium Statistical Mechanics.
.111
1.5.2
Statistical Mechanics of Nonlinear Oscillator Chains
. . . 124
1.5.3
Geometrical Modelling of Continuous Dynamics
.125
1.5.4
Lagrangian Chaos
.128
1.6
Standard Map and Hamiltonian Chaos
.136
1.7
Chaotic Dynamics of Binary Systems
.142
1.7.1
Examples of Dynamical Maps
.144
1.7.2
Correlation Dimension of an Attractor
.148
1.8
Basic Hamiltonian Model of
Biodynamics
.149
vii
Contents
Smale
Horseshoes and Homoclinic Dynamics
.153
2.1
Smale
Horseshoe Orbits and Symbolic Dynamics
.153
2.1.1
Horseshoe Trellis
.157
2.1.2
Trellis-Forced Dynamics
.161
2.1.3
Homoclinic Braid Type
.164
2.2
Homoclinic Classes for Generic Vector-Fields
.165
2.2.1
Lyapunov Stability
.168
2.2.2
Homoclinic Classes
.171
2.3
Complex-Valued
Hénon
Maps and Horseshoes
.174
2.3.1
Complex Henon-Like Maps
.175
2.3.2
Complex Horseshoes
.178
2.4
Chaos in Functional Delay Equations
.181
2.4.1
Poincaré
Maps and Homoclinic Solutions
.184
2.4.2
Starting Value and Targets
.192
2.4.3
Successive Modifications of
g
.199
2.4.4
Transversality
.215
2.4.5
Transversally Homoclinic Solutions
.221
3-Body Problem and Chaos Control
.223
3.1
Mechanical Origin of Chaos
.223
3.1.1
Restricted 3-Body Problem
.224
3.1.2
Scaling and Reduction in the 3-Body Problem
.236
3.1.3
Periodic Solutions of the 3-Body Problem
.239
3.1.4
Bifurcating Periodic Solutions of the 3-Body Problem.
. 240
3.1.5
Bifurcations in Lagrangian Equilibria
.241
3.1.6
Continuation of KAM-Tori
.247
3.1.7
Parametric Resonance and Chaos in Cosmology
.249
3.2
Elements of Chaos Control
.252
3.2.1
Feedback and Non-Feedback Algorithms for Chaos
Control
.252
3.2.2
Exploiting Critical Sensitivity
.256
3.2.3
Lyapunov Exponents and Kaplan-Yorke Dimension
. 257
3.2.4
Kolmogorov-Sinai Entropy
.259
3.2.5
Chaos Control by
Ott,
Grebogi and Yorke (OGY)
.261
3.2.6
Floquet Stability Analysis and OGY Control
.264
3.2.7
Blind Chaos Control
.268
3.2.8
Jerk Functions of Simple Chaotic Flows
.272
3.2.9
Example: Chaos Control in Molecular Dynamics
.275
Phase Transitions and Synergetics
.285
4.1
Phase Transitions, Partition Function and Noise
.285
4.1.1
Equilibrium Phase Transitions
.285
4.1.2
Classification of Phase Transitions
.286
4.1.3
Basic Properties of Phase Transitions
.288
4.1.4
Landau's Theory of Phase Transitions
.290
Contents ix
4.1.5 Partition
Function
.292
4.1.6
Noise-Induced Non-equilibrium Phase Transitions
.299
4.2
Elements of Haken's Synergetics
.306
4.2.1
Phase Transitions
.308
4.2.2
Mezoscopic Derivation of Order Parameters
.310
4.2.3
Example: Synergetic Control of
Biodynamics
.312
4.2.4
Example: Chaotic Psychodynamics of Perception
.313
4.2.5
Kick Dynamics and Dissipation-Fluctuation Theorem
. . 317
4.3
Synergetics of Recurrent and Attractor Neural Networks
.320
4.3.1
Stochastic Dynamics of
Neuronal
Firing States
.322
4.3.2
Synaptic Symmetry and Lyapunov Functions
.327
4.3.3
Detailed Balance and Equilibrium Statistical Mechanics
329
4.3.4
Simple Recurrent Networks with Binary Neurons
.334
4.3.5
Simple Recurrent Networks of Coupled Oscillators
.343
4.3.6
Attractor Neural Networks with Binary Neurons
.350
4.3.7
Attractor Neural Networks with Continuous Neurons
. . 362
4.3.8
Correlation- and Response-Functions
.369
4.3.9
Path-Integral Approach for Complex Dynamics
.378
4.3.10
Hierarchical Self-Programming in Neural Networks
. 399
4.4
Topological Phase Transitions and Hamiltonian Chaos
.406
4.4.1
Phase Transitions in Hamiltonian Systems
.406
4.4.2
Geometry of the Largest Lyapunov Exponent
.408
4.4.3
Euler
Characteristics of Hamiltonian Systems
.412
4.4.4
Pathways to Self-Organization in Human
Biodynamics
. 416
Phase Synchronization in Chaotic Systems
.419
5.1
Lyapunov Vectors and Lyapunov Exponents
.419
5.1.1
Forced
Rössler
Oscillator
.422
5.1.2
Second Lyapunov Exponent: Perturbative Calculation.
. 424
5.2
Phase Synchronization in Coupled Chaotic Oscillators
.426
5.3
Oscillatory Phase
Neurodynamics
.430
5.3.1
Kuramoto Synchronization Model
.432
5.3.2
Lyapunov Chaotic Synchronization
.433
5.4
Synchronization Geometry
.435
5.4.1
Geometry of Coupled Nonlinear Oscillators
.435
5.4.2
Noisy Coupled Nonlinear Oscillators
.439
5.4.3
Synchronization Condition
.448
5.5
Complex Networks and Chaotic Transients
.451
Josephson
Junctions and Quantum Engineering
.457
6.0.1
Josephson
Effect
.460
6.0.2
Pendulum Analog
.461
6.1
Dissipative
Josephson
Junction
.463
6.1.1
Junction Hamiltonian and its Eigenstates
.464
6.1.2
Transition Rate
.466
χ
Contents
6.2
Josephson
Junction Ladder (JJL)
.467
6.2.1
Underdamped JJL
.473
6.3
Synchronization in Arrays of
Josephson
Junctions
.477
6.3.1
Phase Model for Underdamped JJL
.479
6.3.2
Comparison of LKM2 and RCSJ Models
.485
6.3.3
'Small-World' Connections in JJL Arrays
.486
7
Fractals and Fractional Dynamics
.491
7.1
Fractals
.491
7.1.1
Mandelbrot Set
.491
7.2
Robust Strange Non-Chaotic Attractors
.494
7.2.1
Quasi-Periodically Forced Maps
.494
7.2.2
2D Map on a Torus
.497
7.2.3
High Dimensional Maps
.502
7.3
Effective Dynamics in Hamiltonian Systems
.505
7.3.1
Effective Dynamical Invariants
.507
7.4
Formation of Fractal Structure in Many-Body Systems
.508
7.4.1
A Many-Body Hamiltonian
.509
7.4.2
Linear Perturbation Analysis
.509
7.5
Fractional Calculus and Chaos Control
.512
7.5.1
Fractional Calculus
.512
7.5.2
Fractional-Order Chua's Circuit
.514
7.5.3
Feedback Control of Chaos
.515
7.6
Fractional Gradient and Hamiltonian Dynamics
.516
7.6.1
Gradient Systems
.517
7.6.2
Fractional Differential Forms
.518
7.6.3
Fractional Gradient Systems
.519
7.6.4
Hamiltonian Systems
.523
7.6.5
Fractional Hamiltonian Systems
.524
8
Turbulence
.529
8.1
Parameter-Space Analysis of the
Lorenz Attractor.529
8.1.1
Structure of the Parameter-Space
.531
8.1.2
Attractors and Bifurcations
.538
8.2
Periodically-Driven
Lorenz
Dynamics
.539
8.2.1
Toy Model Illustration
.542
8.3 Lorenzian
Diffusion
.545
8.4
Turbulence
.549
8.4.1
Turbulent Flow
.550
8.4.2
The Governing Equations of Turbulence
.552
8.4.3
Global Well-Posedness of the Navier-Stokes Equations
. 553
8.4.4
Spatio-Temporal
Chaos and Turbulence in PDEs
.554
8.4.5
General Fluid Dynamics
.559
8.4.6
Computational Fluid Dynamics
.563
8.5
Turbulence Kinetics
.565
Contents xi
8.5.1
Kinetic Theory
.567
8.5.2
Filtered Kinetic Theory
.570
8.5.3
Hydrodynamic Limit
.572
8.5.4
Hydrodynamic Equations
.574
8.6
Lie Symmetries in the Models of Turbulence
.575
8.6.1
Lie Symmetries and Prolongations on Manifolds
.576
8.6.2
Noether Theorem and Navier-Stokes Equations
.589
8.6.3
Large-Eddy Simulation
.591
8.6.4
Model Analysis
.594
8.6.5
Thermodynamic Consistence
.600
8.6.6
Stability of Turbulence Models
.602
8.7
Advection of Vector-Fields by Chaotic Flows
.603
8.7.1
Advective Fluid Flow
.603
8.7.2
Chaotic Flows
.606
8.8
Brownian Motion and Diffusion
.607
8.8.1
Random Walk Model
.607
8.8.2
More Complicated Transport Processes
.609
8.8.3
Advection-Diffusion
.609
8.8.4
Beyond the Diffusion Coefficient
.614
9
Geometry,
Solitons
and Chaos Field Theory
.617
9.1
Chaotic Dynamics and Riemannian Geometry
.617
9.2
Chaos in Physical Gauge Fields
.620
9.3
Solitions
.625
9.3.1
History of
Solitons in
Brief
.625
9.3.2
The Fermi-Pasta-Ulam Experiments
.630
9.3.3
The Kruskal-Zabusky Experiments
.635
9.3.4
A First Look at the KdV Equation
.638
9.3.5
Split-Stepping KdV
.641
9.3.6 Solitons
from a Pendulum Chain
.643
9.3.7
ID Crystal Soliton
.644
9.3.8 Solitons
and Chaotic Systems
.645
9.4
Chaos Field Theory
.649
References
.653
Index
.689 |
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| any_adam_object_boolean | 1 |
| author | Ivancevic, Vladimir G. Ivancevic, Tijana T. |
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| id | DE-604.BV022933492 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:55:21Z |
| indexdate | 2024-07-20T09:25:36Z |
| institution | BVB |
| isbn | 9781402054556 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016138282 |
| oclc_num | 77077731 |
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| physical | XVI, 700 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
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| publisher | Springer |
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| series | Intelligent systems, control and automation: science and engineering |
| series2 | Intelligent systems, control and automation: science and engineering |
| spelling | Ivancevic, Vladimir G. Verfasser aut High-dimensional chaotic and attractor systems a comprehensive introduction Vladimir G. Ivancevic ; Tijana T. Ivancevic Dordrecht Springer 2007 XVI, 700 S. txt rdacontent n rdamedia nc rdacarrier Intelligent systems, control and automation: science and engineering 32 Atratores larpcal Caos (sistemas dinâmicos) larpcal Dynamics Mechanics, Analytic Attraktor (DE-588)4140563-8 gnd rswk-swf Hochdimensionales System (DE-588)4202326-9 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Chaotisches System (DE-588)4316104-2 s Attraktor (DE-588)4140563-8 s Hochdimensionales System (DE-588)4202326-9 s DE-604 Ivancevic, Tijana T. Verfasser aut Erscheint auch als Online-Ausgabe 978-1-4020-5456-3 Intelligent systems, control and automation: science and engineering 32 (DE-604)BV024977557 32 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2844159&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016138282&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ivancevic, Vladimir G. Ivancevic, Tijana T. High-dimensional chaotic and attractor systems a comprehensive introduction Intelligent systems, control and automation: science and engineering Atratores larpcal Caos (sistemas dinâmicos) larpcal Dynamics Mechanics, Analytic Attraktor (DE-588)4140563-8 gnd Hochdimensionales System (DE-588)4202326-9 gnd Chaotisches System (DE-588)4316104-2 gnd |
| subject_GND | (DE-588)4140563-8 (DE-588)4202326-9 (DE-588)4316104-2 |
| title | High-dimensional chaotic and attractor systems a comprehensive introduction |
| title_auth | High-dimensional chaotic and attractor systems a comprehensive introduction |
| title_exact_search | High-dimensional chaotic and attractor systems a comprehensive introduction |
| title_exact_search_txtP | High-dimensional chaotic and attractor systems a comprehensive introduction |
| title_full | High-dimensional chaotic and attractor systems a comprehensive introduction Vladimir G. Ivancevic ; Tijana T. Ivancevic |
| title_fullStr | High-dimensional chaotic and attractor systems a comprehensive introduction Vladimir G. Ivancevic ; Tijana T. Ivancevic |
| title_full_unstemmed | High-dimensional chaotic and attractor systems a comprehensive introduction Vladimir G. Ivancevic ; Tijana T. Ivancevic |
| title_short | High-dimensional chaotic and attractor systems |
| title_sort | high dimensional chaotic and attractor systems a comprehensive introduction |
| title_sub | a comprehensive introduction |
| topic | Atratores larpcal Caos (sistemas dinâmicos) larpcal Dynamics Mechanics, Analytic Attraktor (DE-588)4140563-8 gnd Hochdimensionales System (DE-588)4202326-9 gnd Chaotisches System (DE-588)4316104-2 gnd |
| topic_facet | Atratores Caos (sistemas dinâmicos) Dynamics Mechanics, Analytic Attraktor Hochdimensionales System Chaotisches System |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2844159&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016138282&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV024977557 |
| work_keys_str_mv | AT ivancevicvladimirg highdimensionalchaoticandattractorsystemsacomprehensiveintroduction AT ivancevictijanat highdimensionalchaoticandattractorsystemsacomprehensiveintroduction |