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Intrinsic ergodicity via obstruction entropies

Published online by Cambridge University Press:  03 April 2013

VAUGHN CLIMENHAGA  and
DANIEL J. THOMPSON
VAUGHN CLIMENHAGA
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204, USA email [email protected]
DANIEL J. THOMPSON
Affiliation:
Department of Mathematics, The Ohio State University, 100 Math Tower, 231 West 18th Avenue, Columbus, Ohio 43210, USA email [email protected]
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Abstract

Bowen showed that a continuous expansive map with specification has a unique measure of maximal entropy. We show that the conclusion remains true under weaker non-uniform versions of these hypotheses. To this end, we introduce the notions of obstructions to expansivity and specification, and show that if the entropy of such obstructions is smaller than the topological entropy of the map, then there is a unique measure of maximal entropy.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 6 , December 2014 , pp. 1816 - 1831
Copyright
Copyright ©2013 Cambridge University Press 

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