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Bowen Measure From Heteroclinic Points

  Published:2011-11-15
 Printed: Dec 2012
  • D. B. Killough,
    Department of Mathematics, Physics, and Engineering, Mount Royal University, Calgary, AB, Canada T3E 6K6
  • I. F. Putnam,
    Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada V8W 3R4
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Abstract

We present a new construction of the entropy-maximizing, invariant probability measure on a Smale space (the Bowen measure). Our construction is based on points that are unstably equivalent to one given point, and stably equivalent to another: heteroclinic points. The spirit of the construction is similar to Bowen's construction from periodic points, though the techniques are very different. We also prove results about the growth rate of certain sets of heteroclinic points, and about the stable and unstable components of the Bowen measure. The approach we take is to prove results through direct computation for the case of a Shift of Finite type, and then use resolving factor maps to extend the results to more general Smale spaces.
Keywords: hyperbolic dynamics, Smale space hyperbolic dynamics, Smale space
MSC Classifications: 37D20, 37B10 show english descriptions Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
Symbolic dynamics [See also 37Cxx, 37Dxx]
37D20 - Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37B10 - Symbolic dynamics [See also 37Cxx, 37Dxx]
 

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