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Textile Systems for Endomorphisms and Automorphisms of the Shift
Masakazu Nasu
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Memoirs of the American Mathematical Society
1995; 215 pp; softcover
Volume: 114
ISBN-10: 0-8218-2606-9
ISBN-13: 978-0-8218-2606-5
List Price: US$49
Individual Members: US$29.40
Institutional Members: US$39.20
Order Code: MEMO/114/546
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One of the major topics in symbolic dynamics is the analysis of the dynamical systems defined by endomorphisms and automorphisms of subshifts. This includes analysis of the dynamical behavior of one-dimensional cellular automata as a special case. In this work, Nasu introduces the notion of a textile system, which is useful in analyzing the dynamical systems defined by endomorphisms and automorphisms of topological Markov shifts, including one-sided ones. The dynamical properties of automorphisms of sofic systems are also studied. Requiring few prerequisites, this work will appeal not only to specialists in symbolic dynamics but also to nonspecialists interested in symbolic dynamics and those interested in analysis of the dynamical behavior of cellular automata.

Readership

Specialists in symbolic dynamics, nonspecialists interested in symbolic dynamics, and those interested in analysis of the dynamical behavior of cellular automata.

Table of Contents

  • Introduction
  • Preliminaries
  • Textile systems
  • Resolving textile systems
  • Sofic textile systems
  • Topological conjugacy between sofic systems
  • LR textile systems
  • Resolvable textile systems
  • Essentially LR automorphisms
  • Similarity
  • Examples
  • References
  • List of notation
  • Index
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