Reversible equivariant Hopf bifurcation
Nenhuma Miniatura disponível
Data
2005-01-01
Orientador
Coorientador
Pós-graduação
Curso de graduação
Título da Revista
ISSN da Revista
Título de Volume
Editor
Springer
Tipo
Artigo
Direito de acesso
Acesso restrito
Resumo
In this paper we study codimension-one Hopf bifurcation from symmetric equilibrium points in reversible equivariant vector fields. Such bifurcations are characterized by a doubly degenerate pair of purely imaginary eigenvalues of the linearization of the vector field at the equilibrium point. The eigenvalue movements near such a degeneracy typically follow one of three scenarios: splitting (from two pairs of imaginary eigenvalues to a quadruplet on the complex plane), passing (on the imaginary axis), or crossing (a quadruplet crossing the imaginary axis). We give a complete description of the behaviour of reversible periodic orbits in the vicinity of such a bifurcation point. For non-reversible periodic solutions. in the case of Hopf bifurcation with crossing eigenvalues. we obtain a generalization of the equivariant Hopf Theorem.
Descrição
Palavras-chave
Idioma
Inglês
Como citar
Archive For Rational Mechanics and Analysis. New York: Springer, v. 175, n. 1, p. 39-84, 2005.
