2017/09/22 by Tiziano Penati, Marco Sansottera, Veronica Danesi
Computer Science · Mathematics · Physics and Astronomy · #Classical mechanics #Computer science #Continuation #Degenerate energy levels #Geometry #Hamiltonian (control theory) #Hamiltonian system #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Periodic orbits #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Quasi periodic #Torus #math-ph #math.DS #math.MP
paper · pdf · doi:10.1016/j.cnsns.2018.02.003
37 pages
arxiv created 2017/09/22 · openalex publication_date 2018/02/08 · arxiv updated 2018/03/14 · openalex created_date 2022/05/12 · openalex updated_date 2026/08/05
We reconsider the classical problem of the continuation of degenerate periodic orbits in Hamiltonian systems. In particular we focus on periodic orbits that arise from the breaking of a completely resonant maximal torus. We here propose a suitable normal form construction that allows to identify and approximate the periodic orbits which survive to the breaking of the resonant torus. Our algorithm allows to treat the continuation of approximate orbits which are at leading order degenerate, hence not covered by classical averaging methods. We discuss possible future extensions and applications to localized periodic orbits in chains of weakly coupled oscillators.