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One-sided almost specification and intrinsic ergodicity

Published online by Cambridge University Press:  18 January 2018

VAUGHN CLIMENHAGA  and
RONNIE PAVLOV
VAUGHN CLIMENHAGA
Affiliation:
Department of Mathematics, University of Houston, 4800 Calhoun St., Houston, TX 77204, USA email [email protected]
RONNIE PAVLOV
Affiliation:
Department of Mathematics, University of Denver, 2290 S. York St., Denver, CO 80208, USA email [email protected]
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Abstract

We define a new property called one-sided almost specification, which lies between the properties of specification and almost specification, and prove that it guarantees intrinsic ergodicity (i.e. uniqueness of the measure of maximal entropy) if the corresponding mistake function $g$ is bounded. We also show that uniqueness may fail for unbounded $g$ such as $\log \log n$. Our results have consequences for almost specification: we prove that almost specification with $g\equiv 1$ implies one-sided almost specification (with $g\equiv 1$) and hence uniqueness. On the other hand, the second author showed recently that almost specification with $g\equiv 4$ does not imply uniqueness.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 9 , September 2019 , pp. 2456 - 2480
Copyright
© Cambridge University Press, 2018 

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