Unstable Entropy and Unstable Pressure for Random Partially Hyperbolic Dynamical Systems

2018/11/30 by Xinsheng Wang, Wang, Xinsheng, Weisheng Wu +3
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Chaos control and synchronization

paper · pdf · doi:10.48550/arxiv.1811.12674

Abstract

Let F be a C² random partially hyperbolic dynamical system. For the unstable foliation, the corresponding unstable metric entropy, unstable topological entropy and unstable pressure via the dynamics of F on the unstable foliation are introduced and investigated. A version of Shannon-McMillan-Breiman Theorem for unstable metric entropy is given, and a variational principle for unstable pressure (and hence for unstable entropy) is obtained. Moreover, as an application of the variational principle, equilibrium states for the unstable pressure including Gibbs u-states are investigated.

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