Hofer's geometry and topological entropy

In this paper we study persistence features of topological entropy and periodic orbit growth Hamiltonian diffeomorphisms on surfaces with respect to Hofer's metric. We exhibit stability these dynamical quantities in a rather strong sense for specific family maps studied by Polterovich Shelukhin. A crucial ingredient comes from enhancement lower bounds the forced point, formulated terms geometric self-intersection number variant Turaev's cobracket free homotopy class that it induces. Those are obtained within framework Le Calvez Tal's forcing theory.