Periodic orbits of Hamiltonian systems linear and hyperbolic at infinity

Başak Z. Gürel

Vol. 271 (2014), No. 1, 159–182

DOI: 10.2140/pjm.2014.271.159

Abstract

We consider Hamiltonian diffeomorphisms of symplectic Euclidean spaces, generated by compactly supported time-dependent perturbations of hyperbolic quadratic forms. We prove that, under some natural assumptions, such a diffeomorphism must have simple periodic orbits of arbitrarily large period when it has fixed points which are not necessary from a homological perspective.

Keywords

periodic orbits, Hamiltonian flows, Floer homology, Conley conjecture

Mathematical Subject Classification 2010

Primary: 37J10, 53D40

Milestones

Received: 27 May 2013

Revised: 28 November 2013

Accepted: 2 December 2013

Published: 10 September 2014