TY - JOUR
T1 - Entropy properties of mostly expanding partially hyperbolic diffeomorphisms
AU - Zhang, Jinhua
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.
PY - 2025/9
Y1 - 2025/9
N2 - The statistical properties of mostly expanding partially hyperbolic diffeomorphisms have been substantially studied. In this paper, we would like to address the entropy properties of mostly expanding partially hyperbolic diffeomorphisms. We prove that for mostly expanding partially hyperbolic diffeomorphisms with minimal strong stable foliation and one-dimensional center bundle, there exists a -open neighborhood of them, in which the topological entropy varies continuously and the intermediate entropy property holds. To prove that, we show that each non-hyperbolic ergodic measure is approached by horseshoes in entropy and in weak-topology.
AB - The statistical properties of mostly expanding partially hyperbolic diffeomorphisms have been substantially studied. In this paper, we would like to address the entropy properties of mostly expanding partially hyperbolic diffeomorphisms. We prove that for mostly expanding partially hyperbolic diffeomorphisms with minimal strong stable foliation and one-dimensional center bundle, there exists a -open neighborhood of them, in which the topological entropy varies continuously and the intermediate entropy property holds. To prove that, we show that each non-hyperbolic ergodic measure is approached by horseshoes in entropy and in weak-topology.
UR - https://www.scopus.com/pages/publications/105014474656
U2 - 10.1007/s00208-025-03243-1
DO - 10.1007/s00208-025-03243-1
M3 - 文章
AN - SCOPUS:105014474656
SN - 0025-5831
VL - 393
SP - 953
EP - 992
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1
ER -