عنوان

Applied symbolic dynamics and chaos /

9789813236431

9789813236448

9813236434

9813236442

9789813236424

9813236426

Applied symbolic dynamics and chaos /

[Book]

Bailin Hao, Weimou Zheng.

Second edition.

Singapore :

World Scientific Publishing Co. Pte. Ltd.,

[2018]

1 online resource

Peking University-World Scientific advanced physics series,

vol. 4

2382-5960 ;

Originally published by Peking University Press in 2014.

Includes bibliographical references and index.

Intro; Contents; Preface to the Second Edition; Preface to the First Edition; 1 Introduction; 1.1 Dynamical Systems; 1.1.1 Phase Space and Orbits; 1.1.2 Parameters and Bifurcation of Dynamical Behavior; 1.1.3 Examples of Dynamical Systems; 1.2 Symbolic Dynamics as Coarse-Grained Description of Dynamics; 1.2.1 Fine-Grained and Coarse-Grained Descriptions; 1.2.2 Symbolic Dynamics as the Simplest Dynamics; 1.3 Abstract versus Applied Symbolic Dynamics; 1.3.1 Abstract Symbolic Dynamics; 1.3.2 Applied Symbolic Dynamics; 1.4 Literature on Symbolic Dynamics; 2 Symbolic Dynamics of Unimodal Maps.

2.1 Symbolic Sequences in Unimodal Maps; 2.1.1 Numerical Orbit and Symbolic Sequence; 2.1.2 Symbolic Sequence and Functional Composition; 2.1.3 The Word-Lifting Technique; 2.2 The Quadratic Map; 2.2.1 An Over-Simplified Population Model; 2.2.2 Bifurcation Diagram of the Quadratic Map; 2.2.3 Dark Lines in the Bifurcation Diagram; 2.3 Ordering of Symbolic Sequences and the Admissibility Condition; 2.3.1 Property of Monotone Functions; 2.3.2 The Ordering Rule; 2.3.3 Dynamical Invariant Range and Kneading Sequence; 2.3.4 The Admissibility Condition; 2.4 The Periodic Window Theorem.

2.4.1 The Periodic Window Theorem; 2.4.2 Construction of Median Words; 2.4.3 The MSS Table of Kneading Sequences; 2.4.4 Nomenclature of Unstable Periodic Orbits; 2.5 Composition Rules; 2.5.1 The ∗-Composition; 2.5.2 Generalized Composition Rule; 2.5.3 Proof of the Generalized Composition Rule; 2.5.4 Applications of the Generalized Composition Rule; 2.5.5 Further Remarks on Composition Rules; 2.6 Coarse-Grained Chaos; 2.6.1 Chaos in the Surjective Unimodal Map; 2.6.2 Chaos in ∞ Maps; 2.7 Topological Entropy; 2.8 Piecewise Linear Maps and Metric Representation of Symbolic Sequences

2.8.1 The Tent Map and Shift Map; 2.8.2 The -Expansion of Real Numbers; 2.8.3 Characteristic Function of the Kneading Sequence; 2.8.4 Mapping of Subintervals and the Stefan Matrix; 2.8.5 Markov Partitions and Generating Partitions; 2.8.6 Metric Representation of Symbolic Sequences; 2.8.7 Piecewise Linear Expanding Map; 3 Maps with Multiple Critical Points; 3.1 General Discussion; 3.1.1 The Ordering Rule; 3.1.2 Construction of a Map from a Given Kneading Sequence; 3.2 The Antisymmetric Cubic Map; 3.2.1 Symbolic Sequences and Their Ordering; 3.2.2 Admissibility Conditions.

3.2.3 Generation of Superstable Median Words; 3.3 Symmetry Breaking and Restoration; 3.3.1 Symmetry Breaking of Symmetric Orbits; 3.3.2 Analysis of Symmetry Restoration; 3.4 The Gap Map; 3.4.1 The Kneading Plane; 3.4.2 Contacts of Even-Odd Type; 3.4.3 Self-Similar Structure in the Kneading Plane; 3.4.4 Criterion for Topological Chaos; 3.5 The Lorenz-Like Map; 3.5.1 Ordering Rule and Admissibility Conditions; 3.5.2 Construction of the Kneading Plane; 3.5.3 Contacts and Intersections; 3.5.4 Farey and Doubling Transformations; 3.6 General Cubic Maps.

3.6.1 Skeleton, Bones and Joints in Kneading Plane.

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"Symbolic dynamics is a coarse-grained description of dynamics. It has been a long-studied chapter of the mathematical theory of dynamical systems, but its abstract formulation has kept many practitioners of physical sciences and engineering from appreciating its simplicity, beauty, and power. At the same time, symbolic dynamics provides almost the only rigorous way to understand global systematics of periodic and, especially, chaotic motion in dynamical systems. In a sense, everyone who enters the field of chaotic dynamics should begin with the study of symbolic dynamics. However, this has not been an easy task for non-mathematicians. On one hand, the method of symbolic dynamics has been developed to such an extent that it may well become a practical tool in studying chaotic dynamics, both on computers and in laboratories. On the other hand, most of the existing literature on symbolic dynamics is mathematics-oriented. This book is an attempt at partially filling up this apparent gap by emphasizing the applied aspects of symbolic dynamics without mathematical rigor."--Publisher's website.

Applied symbolic dynamics and chaos.

9789813236424

Chaotic behavior in systems.

Symbolic dynamics.

Chaotic behavior in systems.

MATHEMATICS-- Topology.

Symbolic dynamics.

MAT-- 038000

Hao, Bailin

Zheng, Wei-Mou

20200823231940.0

pn

[Book]

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