TY - JOUR
T1 - Rigidity of Equilibrium States and Unique Quasi-Ergodicity for Horocyclic Foliations
AU - Carrasco, Pablo D.
AU - Rodriguez-Hertz, Federico
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Brazilian Mathematical Society 2025.
PY - 2025/3
Y1 - 2025/3
N2 - In this paper we prove that for topologically mixing metric Anosov flows their equilibrium states corresponding to Hölder 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 gives another proof of a result of Babillott-Ledrappier.
AB - In this paper we prove that for topologically mixing metric Anosov flows their equilibrium states corresponding to Hölder 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 gives another proof of a result of Babillott-Ledrappier.
UR - https://www.scopus.com/pages/publications/85217807327
UR - https://www.scopus.com/inward/citedby.url?scp=85217807327&partnerID=8YFLogxK
U2 - 10.1007/s00574-025-00440-z
DO - 10.1007/s00574-025-00440-z
M3 - Article
AN - SCOPUS:85217807327
SN - 1678-7544
VL - 56
JO - Bulletin of the Brazilian Mathematical Society
JF - Bulletin of the Brazilian Mathematical Society
IS - 1
M1 - 17
ER -