2021/12/09 by Arnon Chor, Chor, Arnon, Matthias Meiwes +1
Mathematics · #Mathematical Dynamics and Fractals #Homotopy and Cohomology in Algebraic Topology #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.2112.04955
In this article we study persistence features of topological entropy and periodic orbit growth of Hamiltonian diffeomorphisms on surfaces with respect to Hofer's metric. We exhibit stability of these dynamical quantities in a rather strong sense for a specific family of maps introduced by Polterovich and Shelukhin. A crucial ingredient comes from some enhancement of lower bounds for the topological entropy and orbit growth forced by a periodic point, formulated in terms of the geometric self-intersection number and a variant of Turaev's cobracket of the free homotopy class that it induces. Those bounds are obtained within the framework of Le Calvez and Tal's forcing theory.