Periodic orbits for Hamiltonian systems in cotangent bundles

1991/11/11 by Christopher Golé, Golé, Christopher
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math.DS

paper · pdf · doi:10.48550/arxiv.math/9201297

arxiv created 1991/11/11 · openalex publication_date 1991/11/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of at least cl(M) periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold M. These Hamiltonians are not necessarily convex but they satisfy a certain boundary condition given by a Riemannian metric on M. We discretize the variational problem by decomposing the time 1 map into a product of ``symplectic twist maps''. A second theorem deals with homotopically non trivial orbits in manifolds of negative curvature.

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