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Bowen Measure From Heteroclinic Points

Published online by Cambridge University Press:  20 November 2018

D. B. Killough  and
I. F. Putnam
D. B. Killough
Affiliation:
Department of Mathematics, Physics, and Engineering, Mount Royal University, Calgary, AB T3E 6K6 email: bkillough@mtroyal.ca
I. F. Putnam
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4 email: putnam@math.uvic.ca
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Abstract

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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, i.e., 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

37D2037B10hyperbolic dynamicsSmale space
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 64 , Issue 6 , 01 December 2012 , pp. 1341 - 1358
Copyright
Copyright © Canadian Mathematical Society 2012

References

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