$\Gamma -\Sigma -C^0-$determinacy of $\Gamma -\Sigma -C^0-$equivariant bifurcation problems with respect to $\Gamma -\Sigma -C^0-$BD and contact equivalence from the weighted point view

Abstract

In this paper, $C^0$ finite determination of $\Gamma -$equivariant bifurcation problems in the relative case from the weighted point view is being discussed . Some criteria on the $C^0$ finite determination of $\Gamma -$equi-variant bifurcation problems in the relative case are then obtained in terms of an analytic-geometric non-degeneracy condition, which generalize the result on the $C^0$ finite determination of bifurcation problems given by P.B.Percell and P.N.Brown.