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Simplicial Dynamical Systems
 
Ethan Akin City College (CUNY), New York, NY
Simplicial Dynamical Systems
eBook ISBN:  978-1-4704-0258-7
Product Code:  MEMO/140/667.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $36.00
Simplicial Dynamical Systems
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Simplicial Dynamical Systems
Ethan Akin City College (CUNY), New York, NY
eBook ISBN:  978-1-4704-0258-7
Product Code:  MEMO/140/667.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $36.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1401999; 197 pp
    MSC: Primary 54; 58; 34

    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
     
     
    • Chapters
    • 1. Chain recurrence and basic sets
    • 2. Simplicial maps and their local inverses
    • 3. The shift factor maps for a simplicial dynamical system
    • 4. Recurrence and basic set images
    • 5. Invariant measures
    • 6. Generalized simplicial dynamical systems
    • 7. Examples
    • 8. PL roundoffs of a continuous map
    • 9. Nondegenerate maps on manifolds
    • 10. Appendix: Stellar and lunar subdivisions
    • 11. Appendix: Hyperbolicity for relations
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1401999; 197 pp
MSC: Primary 54; 58; 34

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.

  • Chapters
  • 1. Chain recurrence and basic sets
  • 2. Simplicial maps and their local inverses
  • 3. The shift factor maps for a simplicial dynamical system
  • 4. Recurrence and basic set images
  • 5. Invariant measures
  • 6. Generalized simplicial dynamical systems
  • 7. Examples
  • 8. PL roundoffs of a continuous map
  • 9. Nondegenerate maps on manifolds
  • 10. Appendix: Stellar and lunar subdivisions
  • 11. Appendix: Hyperbolicity for relations
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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