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Regularization of the Amended Potential around a Symmetric Configuration


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.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Gabai, David (advisor)
  • Luxemburg, W. A. J. (co-advisor)
Thesis Committee:
  • Marsden, Jerrold E. (chair)
  • Makarov, Nikolai G.
  • Ramakrishnan, Dinakar
  • Gabai, David
  • Luxemburg, W. A. J.
Defense Date:4 October 2001
Record Number:CaltechETD:etd-12122003-115521
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4960
Deposited By: Imported from ETD-db
Deposited On:12 Dec 2003
Last Modified:05 Nov 2021 20:37

Thesis Files

PDF (Garduno_ah_2002.pdf) - Final Version
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