2003•Chinese Annals of Mathematics,series ARequires access

THE UNFOLDING OF MULTIPARAMETER EQUIVARIANT BIFURCATION PROBLEMS WITH RESPECT TO LEFT-RIGHT EQUIVALENCE

LI Yang-cheng

Abstract

Based on the left-right equivalence of smooth map-germs in singularity theory, the present paper introduces a new equivalence relation in the study of equivariant bifurcation problems. It is given that a criterion for the A(Г)-triviality of a one-parameter unfolding of bifurcation problem with a compact Lie group Г as symmetry group. The necessary and sufficient condition for an unfolding of Г-equivariant bifurcation problem to be versal is obtained.

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Key concepts: Equivariant map, Mathematics, Triviality, Bifurcation, Equivalence (formal languages), Pure mathematics, Equivalence relation, Singularity theory