Simplicial Dynamical Systems (Memoirs of the American Mathematical Society)

Simplicial Dynamical Systems (Memoirs of the American Mathematical Society)


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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.


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.

Product Details

  • ISBN13: 9780821813836
  • Format: Paperback
  • ID: 9780821813836
  • ISBN10: 0821813838

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