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Directions in Chaos - Vol. 6
GRAMMATICAL COMPLEXITY AND ONE-DIMENSIONAL DYNAMICAL SYSTEMS
by H-M Xie (Suzhou Univ.)
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.
Contents:
- Strings and Languages:
- Free Monoids
- Dynamical
Languages
- Grammatical Complexity of Unimodal Maps:
- Languages of Unimodal Maps
- Regular Languages of Unimodal Maps
- A General Discussion of Kneading Sequences
- Non-Regular Languages of Unimodal Maps
- DEB of Unimodal Maps
- Topological Entropy of Unimodal Maps
- Grammatical Complexity of Circle Homeomorphisms:
- Languages of Circle Homeomorphisms
- Complexity Levels of Circle Homeomorphisms
- Automata of Circle Homeomorphisms
- Appendices:
- Finite Automata and Regular Languages
- Non-Regular Languages
- L Systems and Languages
Readership: Scientists interested in chaos and nonlinear science.
| 288pp |
Pub. date: Nov 1996 |
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