Periodic Orbits of Hamiltonian Systems Linear and Hyperbolic at Infinity

Abstract

We consider Hamiltonian diffeomorphisms of the Euclidean space, 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.

21 pages; substantially revised, final version; to appear in Pacific Journal of Mathematics

References in corpus (3)

• On Non-contractible Periodic Orbits of Hamiltonian Diffeomorphisms
• Hyperbolic Fixed Points and Periodic Orbits of Hamiltonian Diffeomorphisms
• A symplectic proof of a theorem of Franks

Cited by in corpus (7)

• Hamiltonian Pseudo-rotations of Projective Spaces
• On Non-contractible Periodic Orbits of Hamiltonian Diffeomorphisms
• Non-contractible Periodic Orbits in Hamiltonian Dynamics on Closed Symplectic Manifolds
• On hyperbolic points and periodic orbits of symplectomorphisms
• Existence of noncontractible periodic orbits of Hamiltonian system separating two Lagrangian tori on $T^*\T^n$ with application to non convex Hamiltonian systems
• On Periodic Points of Symplectomorphisms on Surfaces
• Perfect Reeb flows and action-index relations