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kolmogorov property

Ergodic Theory and Dynamical Systems (1)

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1 results

The K-property for some unique equilibrium states in flows and homeomorphisms
Part of
- Dynamical systems with hyperbolic behavior
- Smooth dynamical systems: general theory
BENJAMIN CALL
Journal:

Ergodic Theory and Dynamical Systems / Volume 42 / Issue 8 / August 2022

Published online by Cambridge University Press:

12 November 2021, pp. 2509-2532

Print publication:

August 2022
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We set out some general criteria to prove the K-property, refining the assumptions used in an earlier paper 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.