$Gamma-Sigma-C^{0}-$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

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.