2015/11/23 by Antonella Marchesiello, Giuseppe Pucacco · 11 citations
Mathematics · Physics and Astronomy · #Astro and Planetary Science #Astrophysics and Star Formation Studies #Bifurcation #Classical mechanics #Hamiltonian (control theory) #Hamiltonian system #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Phase space #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Singularity #Singularity theory #astro-ph.IM #math-ph #math.DS #math.MP #nlin.CD
paper · pdf · doi:10.1142/s0218127416300111
published in International Journal of Bifurcation and Chaos 26(04), 1630011 (World Scientific) · 36 pages, 10 figures, accepted on International Journal of Bifurcation and Chaos. arXiv admin note: substantial text overlap with arXiv:1401.2855
arxiv created 2015/11/23 · openalex publication_date 2016/04/01 · arxiv updated 2016/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a general review of the bifurcation sequences of periodic orbits in general position of a family of resonant Hamiltonian normal forms with nearly equal unperturbed frequencies, invariant under [Formula: see text] symmetry. The rich structure of these classical systems is investigated with geometric methods and the relation with the singularity theory approach is also highlighted. The geometric approach is the most straightforward way to obtain a general picture of the phase-space dynamics of the family as is defined by a complete subset in the space of control parameters complying with the symmetry constraint. It is shown how to find an energy-momentum map describing the phase-space structure of each member of the family, a catastrophe map that captures its global features and formal expressions for action-angle variables. Several examples, mainly taken from astrodynamics, are used as applications.