An Introduction to Symbolic Dynamics and Coding

by Douglas Lind, Brian Marcus

Overview

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.

Product Details

ISBN-13:	9781108820288
Publisher:	Cambridge University Press
Publication date:	01/21/2021
Series:	Cambridge Mathematical Library
Edition description:	2nd Revised ed.
Pages:	566
Product dimensions:	5.94(w) x 8.98(h) x 1.18(d)

About the Author

Douglas Lind is Professor Emeritus of Mathematics at the University of Washington. He was department chair, is an Inaugural Fellow of the American Mathematical Society, and served in many governance roles for the Mathematical Sciences Research Institute, including chairing the committee that designed the 2006 addition.

Brian Marcus is Professor of Mathematics at the University of British Columbia. He shared the 1993 Leonard Abraham Prize Paper award of the IEEE Communications Society. He is currently the UBC Site Director of the Pacific Institute for the Mathematical Sciences (PIMS) and is a Fellow of the AMS and IEEE.

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 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.

Editorial Reviews

"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

From the Publisher