Branches of stable three-tori using Hamiltonian methods in Hopf bifurcation on a rhombic lattice

Vivien Kirk*, Jerrold E. Marsden, Mary Silber

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

This paper uses Hamiltonian methods to find and determine the stability of some new solution branches for an equivariant Hopf bifurcation on ℂ4. The normal form has a symmetry group given by the semi-direct product of D2 with T2 × S1. The Hamiltonian part of the normal form is completely integrable and may be analyzed using a system of invariants. The idea of the paper is to perturb relative equilibria in this singular Hamiltonian limit to obtain new three-frequency solutions to the full normal form for parameter values near the Hamiltonian limit. The solutions obtained have fully broken symmetry, that is, they do not lie in fixed point subspaces. The methods developed in this paper allow one to determine the stability of this new branch of solutions. An example shows that the branch of three-tori can be stable.

Original languageEnglish (US)
Pages (from-to)267-302
Number of pages36
JournalDynamical Systems
Volume11
Issue number4
StatePublished - Jan 1 1996

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications

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