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arXiv · 2001.06574

Unstable Entropy and Unstable Pressure for Partially Hyperbolic Endomorphisms

Xinsheng Wang·Weisheng Wu·Yujun Zhu
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Abstract

In this paper, unstable metric entropy, unstable topological entropy and unstable pressure for partially hyperbolic endomorphisms are introduced and investigated. A version of Shannon-McMillan-Breiman Theorem is established, and a variational principle is formulated, which gives a relationship between unstable metric entropy and unstable pressure (unstable topological entropy). As an application of the variational principle, some results on the $u$-equilibrium states are given.

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Xinsheng Wang, Weisheng Wu, Yujun Zhu. 2020-01-18. Unstable Entropy and Unstable Pressure for Partially Hyperbolic Endomorphisms. https://arxiv.org/abs/2001.06574

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