Regularization of the Amended Potential around a Symmetric Configuration

Citation

Garduño, Antonio Hernández (2002) Regularization of the Amended Potential around a Symmetric Configuration. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/NBWA-EQ57. https://resolver.caltech.edu/CaltechETD:etd-12122003-115521

Abstract

Relative equilibria are periodic trajectories that, in a dynamical system with continuous symmetry, correspond to fixed points in the projected dynamics to the quotient space. In Hamiltonian systems with symmetry, it is of interest to understand the structure of relative equilibria near symmetric states. In this context, we give a method that in some cases of simple mechanical systems with compact symmetry group gives information about the relative equilibria bifurcating from a set of relative equilibria with isotropy subgroup isomorphic to S^1. This method is based on the blowing-up of the amended potential.

Thesis Files