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arXiv · 2308.08139

Physical measures for partially hyperbolic diffeomorphisms with mixed hyperbolicity

Zeya Mi·Yongluo Cao
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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.

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Zeya Mi, Yongluo Cao. 2023-08-16. Physical measures for partially hyperbolic diffeomorphisms with mixed hyperbolicity. https://arxiv.org/abs/2308.08139

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