An Introduction to Symbolic Dynamics and Coding
An Introduction to Symbolic Dynamics and Coding
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9781108820288Symbolic dynamics is a rapidly growing area of dynamical systems. Although it originated as a method to study general dynamical systems, it has found significant uses in coding for data storage and transmission as well as in linear algebra. This book is the first general textbook on symbolic dynamics and its applications to coding. It will serve as an introduction to symbolic dynamics for both mathematics and electrical engineering students. Mathematical prerequisites are relatively modest (mainly linear algebra at the undergraduate level) especially for the first half of the book. Topics are carefully developed and motivated with many examples. There are over 500 exercises to test the reader's understanding. The last chapter contains a survey of more advanced topics, and there is a comprehensive bibliography.
- The first textbook on symbolic dynamics
- Assumes only a modest mathematical background (mainly linear algebra at the undergraduate level) and so is accessible to most mathematics and engineering students
- Over 100 figures and 500 exercises to aid the reader's understanding
Reviews & endorsements
"The book is well organized, and lucidly written. It is completely rigorous and yet easy to read....There is a wealth of examples illustrating the definitions and theorems. They are very instructive in helping to understand the principles involved in the proofs. There are also many exercises ranging from simple verifications to hard problems. The book is to be recommended both as an introductory textbook and as a standard reference in the field." Petr Kurka, Mathematical Reviews
"The presentation combines the necessary rigor with a lucidity that makes this book a pleasure to read. It is not only an excellent text for an introductory course, but should be well suited for self-study." F.W. Stallmann, Computing Reviews
"The book is a model of organization and clarity, consistent in pace and tone, with very few errata....The book aims to be accessible to engineers and even strong undergraduates, and the mathematical prerequisites are correspondingly modest....I was pleased with it as a the main source for a one-semester graduate course, supplemented with more advanced material....the book is a very fine and broadly accessible introduction to symbolic dynamics and coding." Mike Boyle, Siam Review
Product details
February 2011Adobe eBook Reader
9780511888656
0 pages
0kg
113 b/w illus.
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- 1. Shift spaces
- 2. Shifts of finite type
- 3. Sofic shifts
- 4. Entropy
- 5. Finite-state codes
- 6. Shifts as dynamical systems
- 7. Conjugacy
- 8. Finite-to-one codes and finite equivalence
- 9. Degrees of codes and almost topological conjugacy
- 10. Embeddings and factorings
- 11. Realization
- 12. Equal entropy factors
- 13. Guide to advanced topics.
