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.
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}
}