Katok’s Entropy Formula of Unstable Metric Entropy for Partially Hyperbolic Diffeomorphisms

Abstract

Katok’s entropy formula is an important formula in entropy theory. It plays significant roles in large deviation theories, multifractal analysis, quantitative recurrence and so on. This paper is devoted to establishing Katok’s entropy formula of unstable metric entropy which is the entropy caused by the unstable part of partially hyperbolic systems. We also construct a similar formula which can be used to study the quantitative recurrence in the unstable manifold for partially hyperbolic diffeomorphisms.

Keywords

Katok’s entropy formula / Unstable metric entropy / Measure decomposition / Partially hyperbolic diffeomorphisms

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Funding

National Natural Science Foundation of China(12101446)