ENGLISH

Grammatical Complexity and One-dimensional Dynamical Systems (Directions in Chaos): 6

By Huimin Xie

Book information

Publisher
World Scientific Publishing Co Pte Ltd
Year
1995
ISBN
9810223986, 9789810223984
Language
english
Format
PDF
Filesize
34 MB (35135576 bytes)
Pages
288\277
Time added
2021-06-28 19:01:43

Description

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. 9789812830678_fmatter 9789812830678_0001 9789812830678_0002 9789812830678_0003 9789812830678_0004 9789812830678_0005 9789812830678_0006 Part II GRAMMATICAL COMPLEXITY OF UNIMODAL MAPS CHAPTER 6 NON-REGULAR LANGUAGES OF UNIMODAL MAPS 6.1 The Language of Feigenbaum Attractor 6.1.1 Renormalization and Kneading Sequence t of Feigenbaum Attractor 6.1.2 Some Properties of t 6 1.3 The Non-Regularity L(t) 6.1.4 The Thue-Morse Sequence 6.2 Grammatical Level of Feigenbaum Attractor 6.2.1 Structure of Language L = C(t) 6.2.2 L is not a Context-Free Language 6.2.3 L is a Context-Sensitive Language 6.3 The Approach of Fibonacci Sequences 6.3.1 Fibonacci Sequences and Cyclic Shifts 6.3.2 Calculation of Cyclic Numbers 6.3.3 Proof of Theorem 6.3.13 6.4 Homomorphisms on Free Submonoids 6.4 1 Two Special Kinds of Homomorphisms 6.4.2 A More General Route 9789812830678_0007 9789812830678_0008 9789812830678_0009 9789812830678_0010 9789812830678_0011 9789812830678_bmatter

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