The K-Property for Some Unique Equilibrium States in Flows and Homeomorphisms

Abstract

We set out some general criteria to prove the K-property, refining the assumptions used in arXiv:1906.09315 for the flow case, and introducing the analogous discrete-time result. We also introduce one-sided $\lambda$-decompositions, as well as multiple techniques for checking the pressure gap required to show the K-property. We apply our results to the family of Mañé diffeomorphisms and the Katok map. Our argument builds on the orbit decomposition theory of Climenhaga and Thompson.

21 pages

References in corpus (1)

• On the non-equivalence of the Bernoulli and K properties in dimension four