On Non-contractible Periodic Orbits of Hamiltonian Diffeomorphisms

Abstract

We prove that any Hamiltonian diffeomorphism of a closed symplectic manifold equipped with an atoroidal symplectic form has simple non-contractible periodic orbits of arbitrarily large period, provided that the diffeomorphism has a non-degenerate (or even isolated and homologically non-trivial) periodic orbit with non-zero homology class and the set of one-periodic orbits in that class is finite.

9 pages

References in corpus (6)

• Hyperbolic Fixed Points and Periodic Orbits of Hamiltonian Diffeomorphisms
• A symplectic proof of a theorem of Franks
• Periodic Orbits of Hamiltonian Systems Linear and Hyperbolic at Infinity
• Non-contractible periodic orbits, Gromov invariants, and Floer-theoretic torsions
• On hyperbolic cohomology classes
• Action-Index Relations for Perfect Hamiltonian Diffeomorphisms

Cited by in corpus (17)

• Hamiltonian Pseudo-rotations of Projective Spaces
• Hyperbolic Fixed Points and Periodic Orbits of Hamiltonian Diffeomorphisms
• Non-contractible Periodic Orbits in Hamiltonian Dynamics on Closed Symplectic Manifolds
• Periodic Orbits of Hamiltonian Systems Linear and Hyperbolic at Infinity
• Non-contractible periodic orbits in Hamiltonian dynamics on tori
• On hyperbolic points and periodic orbits of symplectomorphisms
• On the existence of infinitely many non-contractible periodic orbits of Hamiltonian diffeomorphisms of closed symplectic manifolds
• Floer homology in the cotangent bundle of a closed Finsler manifold and noncontractible periodic orbits
• Symplectic deformations of Floer homology and non-contractible periodic orbits in twisted disc bundles
• On non-contractible periodic orbits for surface homeomorphisms
• On Periodic Points of Symplectomorphisms on Surfaces
• Random Chain Complexes
• Periodic points of rational area-preserving homeomorphisms
• On the Hofer-Zehnder conjecture for non-contractible periodic orbits in Hamiltonian dynamics
• Topological complexity of monotone symplectic manifolds
• Invariant Sets and Hyperbolic Closed Reeb Orbits
• On the Hofer-Zehnder conjecture for semipositive symplectic manifolds