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An Introduction to Symbolic Dynamics and Coding

2nd Edition

Part of Cambridge Mathematical Library

  • Date Published: January 2021
  • availability: In stock
  • format: Paperback
  • isbn: 9781108820288

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  • 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.

    • Assumes only a modest mathematical background (mainly linear algebra at undergraduate level)
    • Contains over 500 exercises, ranging from easy verifications to very challenging problems
    • Includes an addendum (with an extensive bibliography) describing major developments and open problems in symbolic dynamics since the original publication in 1995
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    Product details

    • Edition: 2nd Edition
    • Date Published: January 2021
    • format: Paperback
    • isbn: 9781108820288
    • length: 566 pages
    • dimensions: 228 x 151 x 30 mm
    • weight: 0.81kg
    • availability: In stock
  • 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.

  • Authors

    Douglas Lind, University of Washington
    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, University of British Columbia, Vancouver
    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.

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