Unstable topological entropy in mean u-metrics for partially hyperbolic systems. Issue 3 (3rd July 2021) - Huang, Ping; Wang, Chenwei; Chen, Ercai
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.