Non contractible periodic orbits for generic hamiltonian diffeomorphisms of surfaces

Abstract

Let S be a closed surface of genus g≥1, furnished with an area form ω. We show that there exists an open and dense set Or of the space of Hamiltonian diffeomorphisms of class Cr, 1≤r≤∞, endowed with the Cr-topology, such that every f∈Or possesses infinitely many non contractible periodic orbits. We obtain a positive answer to a question asked by Viktor Ginzburg and Başak Gürel. The proof is a consequence of recent previous works of the authors [LecSa].