Journal article
Pablo D. Carrasco, Federico Rodriguez Hertz
To appear in Israel Journal of Mathematics, 2022
To appear in Israel Journal of Mathematics, 2022
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APA
Carrasco, P. D., & Rodriguez Hertz, F. (2022). Contributions to the ergodic theory of hyperbolic flows: unique ergodicity for quasi-invariant measures and equilibrium states for the time-one map. To Appear in Israel Journal of Mathematics.
Chicago/Turabian
Carrasco, Pablo D., and Federico Rodriguez Hertz. “Contributions to the Ergodic Theory of Hyperbolic Flows: Unique Ergodicity for Quasi-Invariant Measures and Equilibrium States for the Time-One Map.” To appear in Israel Journal of Mathematics (2022).
MLA
Carrasco, Pablo D., and Federico Rodriguez Hertz. “Contributions to the Ergodic Theory of Hyperbolic Flows: Unique Ergodicity for Quasi-Invariant Measures and Equilibrium States for the Time-One Map.” To Appear in Israel Journal of Mathematics, 2022.
We consider the horocyclic flow corresponding to a (topologically mixing) Anosov flow or diffeomorphism, and establish the uniqueness of transverse quasi-invariant measures with Hölder Jacobians. In the same setting, we give a precise characterization of the equilibrium states of the hyperbolic system, showing that existence of a family of Radon measures on the horocyclic foliation such that any probability (invariant or not) having conditionals given by this family, necessarily is the unique equilibrium state of the system.