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EQUILIBRIUM STATES FOR CENTER ISOMETRIES

Part of: Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  02 June 2023

Pablo D. Carrasco Open the ORCID record for Pablo D. Carrasco [Opens in a new window]  and
Federico Rodriguez-Hertz
Pablo D. Carrasco*
Affiliation:
ICEx, UFMG, Belo Horizonte, Minas Gerais, Brazil BR31270-90
Federico Rodriguez-Hertz
Affiliation:
Department of Mathematics - Eberly College of Science, Penn State, State College, Pennsylvania, USA PA 16802 (hertz@math.psu.edu)
*
pdcarrasco@gmail.com
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Abstract

We develop a geometric method to establish the existence and uniqueness of equilibrium states associated to some Hölder potentials for center isometries (as are regular elements of Anosov actions), in particular, the entropy maximizing measure and the SRB measure. A characterization of equilibrium states in terms of their disintegrations along stable and unstable foliations is also given. Finally, we show that the resulting system is isomorphic to a Bernoulli scheme.

Keywords

Partially hyperbolic systemsAnosov actionsequilibrium statesconformal measures

MSC classification

Primary: 37D35: Thermodynamic formalism, variational principles, equilibrium states
Secondary: 37D30: Partially hyperbolic systems and dominated splittings
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 23 , Issue 3 , May 2024 , pp. 1295 - 1355
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Footnotes

P.D.C. is partially supported by FAPEMIG Universal APQ-02160-21.

F. R.-H. is partially supported by NSF grant DMS-1900778

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