An Introduction to Symbolic Dynamics and Coding

Elementary introduction to symbolic dynamics, updated to describe the main advances in the subject since the original publication in 1995.

Douglas Lind (Author), Brian Marcus (Author)

9781108820288, Cambridge University Press

Paperback / softback, published 21 January 2021

566 pages
22.8 x 15.1 x 3 cm, 0.81 kg

Symbolic dynamics is a mature yet rapidly developing area of dynamical systems. It has established strong connections with many areas, including linear algebra, graph theory, probability, group theory, and the theory of computation, as well as data storage, statistical mechanics, and $C^*$-algebras. This Second Edition maintains the introductory character of the original 1995 edition as a general textbook on symbolic dynamics and its applications to coding. It is written at an elementary level and aimed at students, well-established researchers, and experts in mathematics, electrical engineering, and computer science. Topics are carefully developed and motivated with many illustrative examples. There are more than 500 exercises to test the reader's understanding. In addition to a chapter in the First Edition on advanced topics and a comprehensive bibliography, the Second Edition includes a detailed Addendum, with companion bibliography, describing major developments and new research directions since publication of the First Edition.

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 conjugacy
10. Embeddings and factor codes
11. Realization
12. Equal entropy factors
13. Guide to advanced topics
Addendum for the second edition
Bibliography
Addendum bibliography
Notation index
Index.

Subject Areas: Dynamics & statics [PHDT], Coding theory & cryptology [GPJ], Information theory [GPF]