English

The symmetric 1:2 resonance

Chaotic Dynamics 2013-03-13 v1 Instrumentation and Methods for Astrophysics

Abstract

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.

Keywords

Cite

@article{arxiv.1303.2907,
  title  = {The symmetric 1:2 resonance},
  author = {Antonella Marchesiello and Giuseppe Pucacco},
  journal= {arXiv preprint arXiv:1303.2907},
  year   = {2013}
}
R2 v1 2026-06-21T23:40:50.675Z