2014/12/31 by Luca Asselle, Gabriele Benedetti · 1 citation
Mathematics · Physics and Astronomy · #Contractible space #Cotangent bundle #Geometric and Algebraic Topology #Hamiltonian (control theory) #Hamiltonian system #Mathematical Dynamics and Fractals #Periodic orbits #Quantum chaos and dynamical systems #Symplectic geometry #Symplectic manifold #Trigonometric functions #math.DS #math.SG #msc:37J45 #msc:58E05
paper · pdf · doi:10.1142/s1793525316500205
published as Journal of Topology and Analysis 8 (2016), No. 3, 545--570 · 21 pages. We have generalized the results of the previous version to a larger class of manifolds and of energy values. Remarks and comments are very welcome. To appear on Journal of Topology and Analysis
arxiv created 2015/09/30 · openalex publication_date 2015/11/12 · arxiv updated 2016/06/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Let [Formula: see text] be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian [Formula: see text] and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits for such a flow. Our main result asserts that if [Formula: see text] is not aspherical, then contractible periodic orbits exist for almost all energies above the maximum critical value of [Formula: see text].