2009/12/31 by Doris Hein · 2 citations
Mathematics · #math.SG #math.DS
published as J. Sympl. Geom., 10 (2012), 183-202 · 16 pages, 1 figure. Version 2: corrected typos and clarified argument in Section 3, results unchanged
arxiv created 2010/10/10 · arxiv updated 2012/08/07
We prove a generalization of the Conley conjecture: Every Hamiltonian diffeomorphism of a closed symplectic manifold has infinitely many periodic orbits if the first Chern class vanishes over the second fundamental group. In particular, we this removes the rationality condition from similar results. The proof in the irrational case involves several new ideas including the definition and the properties of the filtered Floer homology for Hamiltonians on irrational manifolds. We also develop a method of localizing the filtered Floer homology for short action intervals using a direct sum decomposition, where one of the summands only depends on the behavior of the Hamiltonian in a fixed open set.