(r, s)-STABILITY OF UNFOLDING OF Γ-EQUIVARIANT BIFURCATION PROBLEM

Abstract In this paper, the Γ-equivariant ( s , t )-equivalence relation and Γ-equivariant infinitesimally ( r, s )-stability of Γ-equivariant bifurcation problem are defined. The criterion for Γ-equivariant infinitesimally ( r, s )-stability is proven when Γ is a compact finite Lie group. Transversality condition is used to characterize the stability.