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

TL;DR

This paper investigates the $C^{0}$ finite determination of $ ext{Gamma}$-equivariant bifurcation problems in a weighted setting, providing new criteria that extend previous results to a relative case with geometric non-degeneracy conditions.

Contribution

It introduces criteria for $C^{0}$ finite determination of $ ext{Gamma}$-equivariant bifurcation problems in the relative case, generalizing earlier work by Percell and Brown.

Findings

Established criteria based on analytic-geometric non-degeneracy conditions.

Extended finite determination results to the weighted, relative case.

Generalized previous bifurcation analysis results.

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.