Grammatical Complexity and One-Dimensional Dynamical Systems

By: Bailin Hao (Editor), Huimin Xie

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Hardcover | 1 December 1995

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Hardcover
290 Pages

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22.86 x 15.24 x 1.75

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A combinatorial method is developed in this book to explore the mysteries of chaos, which has became a topic of science since 1975. Using tools from theoretical computer science, formal languages and automata, the complexity of symbolic behaviors of dynamical systems is classified and analysed thoroughly. This book is mainly devoted to explanation of this method and apply it to one-dimensional dynamical systems, including the circle and interval maps, which are typical in exhibiting complex behavior through simple iterated calculations. The knowledge for reading it is self-contained in the book.

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Non-Fiction Mathematics Applied Mathematics Chaos Theory Calculus & Mathematical Analysis Differential Calculus & Equations Combinatorics & Graph Theory Science Physics Classical Mathematics Booktopia Publisher Services World Scientific Publishing

Preface
Strings and Languages	p. 1
Free Monoids	p. 3
Dynamical Languages	p. 13
Grammatical Complexity of Unimodal Maps	p. 37
Languages of Unimodal Maps	p. 39
Regular Languages of Unimodal Maps	p. 63
A General Discussion of Kneading Sequences	p. 97
Non-Regular Languages of Unimodal Maps	p. 111
DEB of Unimodal Maps	p. 145
Topological Entropy of Unimodal Maps	p. 161
Grammatical Complexity of Circle Homeomorphisms	p. 179
Languages of Circle Homeomorphisms	p. 181
Complexity Levels of Circle Homeomorphisms	p. 197
Automata of Circle Homeomorphisms	p. 209
Finite Automata and Regular Languages	p. 227
Non-Regular Languages	p. 241
L Systems and Languages	p. 253
References	p. 259
Symbols Index	p. 269
Subject Index	p. 271
Table of Contents provided by Blackwell. All Rights Reserved.

Grammatical Complexity and One-Dimensional Dynamical Systems

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Hardcover

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