Journal article
Pablo D. Carrasco, Federico Rodriguez-Hertz
arXiv:2304.13384
arXiv:2304.13384
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APA
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Carrasco, P. D., & Rodriguez-Hertz, F. Rigidity of equilibrium states and unique quasi-ergodicity for horocyclic foliations. ArXiv:2304.13384.
Chicago/Turabian
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Carrasco, Pablo D., and Federico Rodriguez-Hertz. “Rigidity of Equilibrium States and Unique Quasi-Ergodicity for Horocyclic Foliations.” arXiv:2304.13384 (n.d.).
MLA
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Carrasco, Pablo D., and Federico Rodriguez-Hertz. “Rigidity of Equilibrium States and Unique Quasi-Ergodicity for Horocyclic Foliations.” ArXiv:2304.13384.
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@article{pablo-a,
title = {Rigidity of equilibrium states and unique quasi-ergodicity for horocyclic foliations},
journal = {arXiv:2304.13384},
author = {Carrasco, Pablo D. and Rodriguez-Hertz, Federico}
}
In this paper we prove that for topologically mixing Anosov flows their equilibrium states corresponding to Höllder potentials satisfy a strong rigidity property: they are determined only by their disintegrations on (strong) stable or unstable leaves.
As a consequence we deduce: the corresponding horocyclic foliations of such systems are uniquely quasi-ergodic, provided that the corresponding Jacobian is Hölder, without any restriction on the dimension of the invariant distributions. This generalizes a classical result due to Babillott and Ledrappier for the geodesic flow of hyperbolic manifolds.
We rely on symbolic dynamics and on recent methods developed by the authors.
As a consequence we deduce: the corresponding horocyclic foliations of such systems are uniquely quasi-ergodic, provided that the corresponding Jacobian is Hölder, without any restriction on the dimension of the invariant distributions. This generalizes a classical result due to Babillott and Ledrappier for the geodesic flow of hyperbolic manifolds.
We rely on symbolic dynamics and on recent methods developed by the authors.
