Unstable topological entropy in mean u-metrics for partially hyperbolic systems. Issue 3 (3rd July 2021)

• Record Type: Journal Article
• Authors: Huang, Ping; Wang, Chenwei; Chen, Ercai
• Is Part Of: Dynamical systems. Volume 36:Issue 3(2021)
• Page Start: 387
• Page End: 403
• Publication Date: 2021-07-03
• Subjects: Unstable topological entropy -- mean u-metrics -- Katok's entropy formula -- variational principle -- partially hyperbolic systems; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2021.1923659
• Languages: English
• ISSNs: 1468-9367

Abstract

Abstract : In this paper, we give the definition of unstable topological entropy in mean u -metrics (the mean metrics in the unstable manifold) for partially hyperbolic systems. By establishing Katok's entropy formula of unstable metric entropy in mean u -metrics, we prove that the new unstable topological entropy is equal to the unstable topological entropy defined in Bowen u -metrics (the Bowen metrics in the unstable manifold). Finally, we obtain the variational principle related to the unstable topological entropy defined in mean u -metrics and unstable metric entropy, which states that the unstable topological entropy defined in mean u-metrics is the supremum of the unstable metric entropy taken over all invariant measures.