Hamiltonian Relative Equilibria with Continuous Isotropy
Dynamical Systems
2015-09-17 v1
Abstract
In symmetric Hamiltonian systems, relative equilibria usually arise in continuous families. The geometry of these families in the setting of free actions of the symmetry group is well-understood. Here we consider the question for non-free actions. Some results are already known in this direction, and we use the so called bundle equations to provide a systematic treatment of this question which both consolidates the known results, extending the scope of the results to deal with non-compact symmetry groups, as well as producing new results. Specifically we address questions about the stability, persistence and bifurcations of these relative equilibria.
Cite
@article{arxiv.1509.04961,
title = {Hamiltonian Relative Equilibria with Continuous Isotropy},
author = {James Montaldi and Miguel Rodriguez-Olmos},
journal= {arXiv preprint arXiv:1509.04961},
year = {2015}
}