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- Title
Unstable entropy and unstable pressure for random partially hyperbolic dynamical systems.
- Authors
Wang, Xinsheng; Wu, Weisheng; Zhu, Yujun
- Abstract
Let ℱ be a C 2 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.
- Subjects
DYNAMICAL systems; ENTROPY; VARIATIONAL principles; RANDOM dynamical systems; TOPOLOGICAL entropy
- Publication
Stochastics & Dynamics, 2021, Vol 21, Issue 5, p1
- ISSN
0219-4937
- Publication type
Article
- DOI
10.1142/S0219493721500210