Journal article
Pablo D. Carrasco, Federico Rodriguez-Hertz
Bulletin of the B.M.S., Volume 56
Bulletin of the B.M.S., Volume 56
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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. Bulletin of the B.M.S., Volume 56. https://doi.org/10.1007/s00574-025-00440-z
Chicago/Turabian
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Carrasco, Pablo D., and Federico Rodriguez-Hertz. “Rigidity of Equilibrium States and Unique Quasi-Ergodicity for Horocyclic Foliations.” Bulletin of the B.M.S. Volume 56 (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.” Bulletin of the B.M.S., vol. Volume 56, doi:10.1007/s00574-025-00440-z.
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@article{pablo-a,
title = {Rigidity of equilibrium states and unique quasi-ergodicity for horocyclic foliations},
journal = {Bulletin of the B.M.S.},
volume = {Volume 56},
doi = {10.1007/s00574-025-00440-z},
author = {Carrasco, Pablo D. and Rodriguez-Hertz, Federico}
}
In this paper we prove that for topologically mixing metric Anosov flows their equilibrium states corresponding to H\"older 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 H\"older, without any restriction on the dimension of the invariant distributions. This gives another proof of a result of Babillott-Ledrappier.
As a consequence we deduce: the corresponding horocyclic foliations of such systems are uniquely quasi-ergodic, provided that the corresponding Jacobian is H\"older, without any restriction on the dimension of the invariant distributions. This gives another proof of a result of Babillott-Ledrappier.