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An Introduction to Symbolic Dynamics and Coding
Symbolic 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.
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.
Brief Description:
This first textbook on this important subject is suitable for both engineering and mathematics students.
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