Bifurcation of relative equilibria in mechanical systems with symmetry
Abstract
The relative equilibria of a symmetric Hamiltonian dynamical system are the critical points of the so-called augmented Hamiltonian. The underlying geometric structure of the system is used to decompose the critical point equations and construct a collection of implicitly defined functions and reduced equations describing the set of relative equilibria in a neighborhood of a given relative equilibrium. The structure of the reduced equations is studied in a few relevant situations. In particular, a persistence result of Lerman and Singer [LS98] is generalized to the framework of Abelian proper actions. Also, a Hamiltonian version of the Equivariant Branching Lemma and a study of bifurcations with maximal isotropy are presented. An elementary example is presented to illustrate the use of this approach.
Keywords
Cite
@article{arxiv.math/9912232,
title = {Bifurcation of relative equilibria in mechanical systems with symmetry},
author = {Pascal Chossat and Debra Lewis and Juan-Pablo Ortega and Tudor S. Ratiu},
journal= {arXiv preprint arXiv:math/9912232},
year = {2007}
}
Comments
32 pages