2013/02/01 by Antonella Marchesiello, Giuseppe Pucacco
Mathematics · Physics and Astronomy · #Class (philosophy) #Classical mechanics #Computer science #General position #Geometry #Hamiltonian (control theory) #Hamiltonian system #Homogeneous space #Mathematical analysis #Mathematical optimization #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Periodic orbits #Phase space #Physics #Position (finance) #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Reflection (computer programming) #Resonance (particle physics) #Space (punctuation) #astro-ph.IM #nlin.CD
paper · pdf · doi:10.1140/epjp/i2013-13021-5
published as Eur. Phys. J. Plus (2013) 128: 21
openalex publication_date 2013/02/01 · arxiv created 2013/03/12 · arxiv updated 2013/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper illustrates the application of Lie transform normal-form theory to the construction of the 1:2 resonant normal form corresponding to a wide class of natural Hamiltonian systems. We show how to compute the bifurcations of the main periodic orbits in a potential with double reflection symmetries. The stability analysis of the normal modes and of the periodic orbits in general position allows us to get overall informations on the phase-space structure of systems in which this resonance is dominating. As an example we apply these results to a class of models useful as galactic potentials.