2000/11/01 by Viktor L. Ginzburg, Ginzburg, Viktor L., Ely Kerman +1
Mathematics · Physics and Astronomy · #58F05(primary) #58F22(secondary) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG) #math.DG #math.DS #math.SG
paper · pdf · doi:10.48550/arxiv.math/0011011
19 pages, 1 figure
arxiv created 2000/11/01 · openalex publication_date 2000/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For Hamiltonian flows we establish the existence of periodic orbits on a sequence of level sets approaching a Bott-nondegenerate symplectic extremum of the Hamiltonian. As a consequence, we show that a charge on a compact manifold with a nondegenerate (i.e. symplectic) magnetic field has periodic orbits on a sequence of energy levels converging to zero.