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The K-property for some unique equilibrium states in flows and homeomorphisms

Part of: Dynamical systems with hyperbolic behavior Smooth dynamical systems: general theory

Published online by Cambridge University Press:  12 November 2021

BENJAMIN CALL Open the ORCID record for BENJAMIN CALL [Opens in a new window]
BENJAMIN CALL*
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH43210, USA
*
e-mail: call.119@buckeyemail.osu.edu
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Abstract

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.

Keywords

equilibrium statesthermodynamic formalismKolmogorov property

MSC classification

Primary: 37D35: Thermodynamic formalism, variational principles, equilibrium states
Secondary: 37C40: Smooth ergodic theory, invariant measures 37D30: Partially hyperbolic systems and dominated splittings
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 8 , August 2022 , pp. 2509 - 2532
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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