Invariants for bifurcations

• Tipo: Artigo em Revista Científica Internacional
• Data: 2006

Autores

Labouriau, IS (Autor) FCUP; Ruas, MAS (Autor) Outra

Revista

Título: Houston Journal of Mathematics

Vol. 32 Nº 2

Páginas: 445-458

ISSN: 0362-1588

Editora: University of Houston

Indexação

ISI Web of Knowledge - 0 Citações

Scopus - 0 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: P-004-PT3

Abstract (EN): Bifurcation problems with one parameter are studied here. We develop a method for computing a topological invariant, the number of fold points in a stable one-parameter unfolding for any given bifurcation of finite codimension. We introduce another topological invariant, the algebraic number of folds. The invariant gives the number of complex solutions to the equations of fold points in a stabilization, an upper bound for the number of fold points in any unfolding. It can be computed by algebraic methods, we show that it is finite for germs of finite codimension. An open question is whether this value is always attained as the maximum number of fold points in a stable unfolding. We compute these two invariants for simple bifurcations in one dimension, answering the question above in the affirmative. We discuss other invariants in the literature and verify that the algebraic number of folds and the Milnor number form a complete set of invariants for simple bifurcations in one dimension.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 14