TY - JOUR
T1 - Contributions to the ergodic theory of hyperbolic flows
T2 - unique ergodicity for quasi-invariant measures and equilibrium states for the time-one map
AU - Carrasco, Pablo D.
AU - Rodriguez-Hertz, Federico
N1 - Publisher Copyright:
© The Hebrew University of Jerusalem 2023.
PY - 2024/6
Y1 - 2024/6
N2 - 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.
AB - 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.
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U2 - 10.1007/s11856-023-2588-3
DO - 10.1007/s11856-023-2588-3
M3 - Article
AN - SCOPUS:85180209510
SN - 0021-2172
VL - 261
SP - 589
EP - 612
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 2
ER -