Rigidity of equilibrium states and unique quasi-ergodicity for horocyclic foliations

Journal article

Pablo D. Carrasco, Federico Rodriguez-Hertz
to appear in Bul. B.M.S.

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APA Click to copy
Carrasco, P. D., & Rodriguez-Hertz, F. Rigidity of equilibrium states and unique quasi-ergodicity for horocyclic foliations. To Appear in Bul. B.M.S. https://doi.org/10.1007/s00574-025-00440-z

Chicago/Turabian Click to copy
Carrasco, Pablo D., and Federico Rodriguez-Hertz. “Rigidity of Equilibrium States and Unique Quasi-Ergodicity for Horocyclic Foliations.” to appear in Bul. B.M.S. (n.d.).

MLA Click to copy
Carrasco, Pablo D., and Federico Rodriguez-Hertz. “Rigidity of Equilibrium States and Unique Quasi-Ergodicity for Horocyclic Foliations.” To Appear in Bul. B.M.S., doi:10.1007/s00574-025-00440-z.

BibTeX Click to copy

@article{pablo-a,
  title = {Rigidity of equilibrium states and unique quasi-ergodicity for horocyclic foliations},
  journal = {to appear in Bul. B.M.S.},
  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.