Journal article
Pablo D. Carrasco, Federico Rodriguez Hertz
Israel Journal of Mathematics, 2023
Israel Journal of Mathematics, 2023
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APA
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Carrasco, P. D., & Rodriguez Hertz, F. (2023). Contributions to the ergodic theory of hyperbolic flows: unique ergodicity for quasi-invariant measures and equilibrium states for the time-one map. Israel Journal of Mathematics. https://doi.org/10.1007/s11856-023-2588-3
Chicago/Turabian
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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.” Israel Journal of Mathematics (2023).
MLA
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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.” Israel Journal of Mathematics, 2023, doi:10.1007/s11856-023-2588-3.
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@article{carrasco2023a,
title = {Contributions to the ergodic theory of hyperbolic flows: unique ergodicity for quasi-invariant measures and equilibrium states for the time-one map},
year = {2023},
journal = {Israel Journal of Mathematics},
doi = {10.1007/s11856-023-2588-3},
author = {Carrasco, Pablo D. and Rodriguez Hertz, Federico}
}
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.
