Invariants for bifurcations

• Type: Article in International Scientific Journal
• Date: 2006

Authors

Labouriau, IS (Author) FCUP; Ruas, MAS (Author) Other

Journal

Title: Houston Journal of Mathematics

Vol. 32 No. 2

Pages: 445-458

ISSN: 0362-1588

Publisher: University of Houston

Indexing

ISI Web of Knowledge - 0 Citations

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Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14