The Resource Robust chaos and its applications, Elhadj Zeraoulia, Julien Clinton Sprott, (electronic resource)

Robust chaos and its applications, Elhadj Zeraoulia, Julien Clinton Sprott, (electronic resource)

Label
Robust chaos and its applications
Title
Robust chaos and its applications
Statement of responsibility
Elhadj Zeraoulia, Julien Clinton Sprott
Creator
Contributor
Subject
Genre
Language
  • eng
  • eng
Summary
Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mat
Member of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Zeraoulia, Elhadj
Dewey number
515.39
Illustrations
illustrations
Index
index present
Language note
English
LC call number
Q172.5.C45
LC item number
Z47 2012
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Sprott, Julien C
Series statement
World Scientific series on nonlinear science. Series A, Monographs and treatises,
Series volume
v. 79
http://library.link/vocab/subjectName
Chaotic behavior in systems
Label
Robust chaos and its applications, Elhadj Zeraoulia, Julien Clinton Sprott, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Preface; Contents; 1. Poincar ́e Map Technique, Smale Horseshoe, and Symbolic Dynamics; 1.1 Poincar ́e and generalized Poincar ́e mappings; 1.2 Interval methods for calculating Poincar ́e mappings; 1.2.1 Existence of periodic orbits; 1.2.2 Interval arithmetic; 1.3 Smale horseshoe; 1.3.1 Dynamics of the horseshoe map; 1.4 Symbolic dynamics; 1.4.1 The method of fixed point index; 1.4.1.1 Periodic points of the TS-map; 1.4.1.2 Existence of semi-conjugacy; 1.5 Exercises; 2. Robustness of Chaos; 2.1 Strange attractors; 2.1.1 Concepts and definitions; 2.1.2 Robust chaos; 2.1.3 Domains of attraction
  • 2.2 Density and robustness of chaos2.3 Persistence and robustness of chaos; 2.4 Exercises; 3. Statistical Properties of Chaotic Attractors; 3.1 Entropies; 3.1.1 Lebesgue (volume) measure; 3.1.2 Physical (or Sinai-Ruelle-Bowen) measure; 3.1.3 Hausdorff dimension; 3.1.4 The topological entropy; 3.1.5 Lyapunov exponent; 3.2 Ergodic theory; 3.3 Statistical properties of chaotic attractors; 3.3.1 Autocorrelation function (ACF); 3.3.2 Correlations; 3.4 Exercises; 4. Structural Stability; 4.1 The concept of structural stability; 4.1.1 Conditions for structural stability
  • 4.1.2 A proof of Anosov's theorem on structural stability of diffeomorphisms4.2 Exercises; 5. Transversality, Invariant Foliation, and the Shadowing Lemma; 5.1 Transversality; 5.2 Invariant foliation; 5.3 Shadowing lemma; 5.3.1 Homoclinic orbits and shadowing; 5.3.2 Shilnikov criterion for the existence of chaos; 5.4 Exercises; 6. Chaotic Attractors with Hyperbolic Structure; 6.1 Hyperbolic dynamics; 6.1.1 Concepts and definitions; 6.1.2 Anosov diffeomorphisms and Anosov flows; 6.2 Anosov diffeomorphisms on the torus Tn; 6.2.1 Anosov automorphisms; 6.2.2 Structure of Anosov diffeomorphisms
  • 6.2.3 Anosov torus Tn with a hyperbolic structure6.2.4 Expanding maps; 6.2.5 The Blaschke product; 6.2.6 The Bernoulli map; 6.2.7 The Arnold cat map; 6.3 Classification of strange attractors of dynamical systems; 6.4 Properties of hyperbolic chaotic attractors; 6.4.1 Geodesic flows on compact smooth manifolds; 6.4.2 The solenoid attractor; 6.4.3 The Smale-Williams solenoid; 6.4.4 Plykin attractor; 6.5 Proof of the hyperbolicity of the logistic map for μ > 4; 6.6 Generalized hyperbolic attractors; 6.7 Generating hyperbolic attractors
  • 6.8 Density of hyperbolicity and homoclinic bifurcations in arbitrary dimension6.9 Hyperbolicity tests; 6.9.1 Numerical procedure; 6.9.2 Testing hyperbolicity of the H ́enon map; 6.9.3 Testing hyperbolicity of the forced damped pendulum; 6.10 Uniform hyperbolicity test; 6.11 Exercises; 7. Robust Chaos in Hyperbolic Systems; 7.1 Modeling hyperbolic attractors; 7.1.1 Modeling the Smale-Williams attractor; 7.1.2 Testing hyperbolicity of system (7.1); 7.1.3 Numerical verification of the hyperbolicity of system (7.1); 7.1.4 Modeling the Arnold cat map; 7.1.5 Modeling the Bernoulli map
  • 7.1.6 Modeling Plykin's attractor
Dimensions
unknown
Extent
1 online resource (473 p.)
Form of item
online
Isbn
9789814374088
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2550000000087703
  • (EBL)846146
  • (SSID)ssj0000647482
  • (PQKBManifestationID)11383582
  • (PQKBTitleCode)TC0000647482
  • (PQKBWorkID)10593481
  • (PQKB)10876822
  • (MiAaPQ)EBC846146
  • (EXLCZ)992550000000087703
Label
Robust chaos and its applications, Elhadj Zeraoulia, Julien Clinton Sprott, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Preface; Contents; 1. Poincar ́e Map Technique, Smale Horseshoe, and Symbolic Dynamics; 1.1 Poincar ́e and generalized Poincar ́e mappings; 1.2 Interval methods for calculating Poincar ́e mappings; 1.2.1 Existence of periodic orbits; 1.2.2 Interval arithmetic; 1.3 Smale horseshoe; 1.3.1 Dynamics of the horseshoe map; 1.4 Symbolic dynamics; 1.4.1 The method of fixed point index; 1.4.1.1 Periodic points of the TS-map; 1.4.1.2 Existence of semi-conjugacy; 1.5 Exercises; 2. Robustness of Chaos; 2.1 Strange attractors; 2.1.1 Concepts and definitions; 2.1.2 Robust chaos; 2.1.3 Domains of attraction
  • 2.2 Density and robustness of chaos2.3 Persistence and robustness of chaos; 2.4 Exercises; 3. Statistical Properties of Chaotic Attractors; 3.1 Entropies; 3.1.1 Lebesgue (volume) measure; 3.1.2 Physical (or Sinai-Ruelle-Bowen) measure; 3.1.3 Hausdorff dimension; 3.1.4 The topological entropy; 3.1.5 Lyapunov exponent; 3.2 Ergodic theory; 3.3 Statistical properties of chaotic attractors; 3.3.1 Autocorrelation function (ACF); 3.3.2 Correlations; 3.4 Exercises; 4. Structural Stability; 4.1 The concept of structural stability; 4.1.1 Conditions for structural stability
  • 4.1.2 A proof of Anosov's theorem on structural stability of diffeomorphisms4.2 Exercises; 5. Transversality, Invariant Foliation, and the Shadowing Lemma; 5.1 Transversality; 5.2 Invariant foliation; 5.3 Shadowing lemma; 5.3.1 Homoclinic orbits and shadowing; 5.3.2 Shilnikov criterion for the existence of chaos; 5.4 Exercises; 6. Chaotic Attractors with Hyperbolic Structure; 6.1 Hyperbolic dynamics; 6.1.1 Concepts and definitions; 6.1.2 Anosov diffeomorphisms and Anosov flows; 6.2 Anosov diffeomorphisms on the torus Tn; 6.2.1 Anosov automorphisms; 6.2.2 Structure of Anosov diffeomorphisms
  • 6.2.3 Anosov torus Tn with a hyperbolic structure6.2.4 Expanding maps; 6.2.5 The Blaschke product; 6.2.6 The Bernoulli map; 6.2.7 The Arnold cat map; 6.3 Classification of strange attractors of dynamical systems; 6.4 Properties of hyperbolic chaotic attractors; 6.4.1 Geodesic flows on compact smooth manifolds; 6.4.2 The solenoid attractor; 6.4.3 The Smale-Williams solenoid; 6.4.4 Plykin attractor; 6.5 Proof of the hyperbolicity of the logistic map for μ > 4; 6.6 Generalized hyperbolic attractors; 6.7 Generating hyperbolic attractors
  • 6.8 Density of hyperbolicity and homoclinic bifurcations in arbitrary dimension6.9 Hyperbolicity tests; 6.9.1 Numerical procedure; 6.9.2 Testing hyperbolicity of the H ́enon map; 6.9.3 Testing hyperbolicity of the forced damped pendulum; 6.10 Uniform hyperbolicity test; 6.11 Exercises; 7. Robust Chaos in Hyperbolic Systems; 7.1 Modeling hyperbolic attractors; 7.1.1 Modeling the Smale-Williams attractor; 7.1.2 Testing hyperbolicity of system (7.1); 7.1.3 Numerical verification of the hyperbolicity of system (7.1); 7.1.4 Modeling the Arnold cat map; 7.1.5 Modeling the Bernoulli map
  • 7.1.6 Modeling Plykin's attractor
Dimensions
unknown
Extent
1 online resource (473 p.)
Form of item
online
Isbn
9789814374088
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2550000000087703
  • (EBL)846146
  • (SSID)ssj0000647482
  • (PQKBManifestationID)11383582
  • (PQKBTitleCode)TC0000647482
  • (PQKBWorkID)10593481
  • (PQKB)10876822
  • (MiAaPQ)EBC846146
  • (EXLCZ)992550000000087703

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