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partially hyperbolic systems

Journal of the Institute of Mathematics of Jussieu (1)

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EQUILIBRIUM STATES FOR CENTER ISOMETRIES
Part of
- Dynamical systems with hyperbolic behavior
Pablo D. Carrasco, Federico Rodriguez-Hertz
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 23 / Issue 3 / May 2024

Published online by Cambridge University Press:

02 June 2023, pp. 1295-1355

Print publication:

May 2024
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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.