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Simplicial Dynamical Systems
Ethan Akin, City College (CUNY), New York, NY
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Memoirs of the American Mathematical Society
1999; 197 pp; softcover
Volume: 140
ISBN-10: 0-8218-1383-8
ISBN-13: 978-0-8218-1383-6
List Price: US$57
Individual Members: US$34.20
Institutional Members: US$45.60
Order Code: MEMO/140/667
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Abstract

A simplicial dynamical system is a simplicial map \(g:K^* \rightarrow K\) where \(K\) is a finite simplicial complex triangulating a compact polyhedron \(X\) and \(K^*\) is a proper subdivision of \(K\), e.g. the barycentric or any further subdivision. The dynamics of the associated piecewise linear map \(g: X X\) can be analyzed by using certain naturally related subshifts of finite type. Any continuous map on \(X\) can be \(C^0\) approximated by such systems. Other examples yield interesting subshift constructions.

Readership

Graduate students and research mathematicians working in topological dynamics.

Table of Contents

  • Introduction
  • Chain recurrence and basic sets
  • Simplicial maps and their local inverses
  • The shift factor maps for a simplicial dynamical system
  • Recurrence and basic set images
  • Invariant measures
  • Generalized simplicial dynamical systems
  • Examples
  • PL roundoffs of a continuous map
  • Nondegenerate maps on manifolds
  • Appendix: Stellar and lunar subdivisions
  • Appendix: Hyperbolicity for relations
  • References
  • Index
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