Physical measures for partially hyperbolic diffeomorphisms with mixed hyperbolicity
Dynamical Systems
2023-08-17 v1
Abstract
We study the partially hyperbolic diffeomorphims whose center direction admits the u-definite property in the sense that all the central Lyapunov exponents of each ergodic Gibbs u-state are either all positive or all negative. We prove that for this kind of partially hyperbolic diffeomorphisms, there are finitely many physical measures, whose basins cover a full Lebesgue measure subset of the ambient space.
Cite
@article{arxiv.2308.08139,
title = {Physical measures for partially hyperbolic diffeomorphisms with mixed hyperbolicity},
author = {Zeya Mi and Yongluo Cao},
journal= {arXiv preprint arXiv:2308.08139},
year = {2023}
}