The k-Zero Bifurcation Theorem for m-Parameterized Systems

Abstract

Given an [Formula: see text]-parameterized family of [Formula: see text]-dimensional vector fields, with an equilibrium point with linearization of eigenvalue zero with algebraic multiplicity [Formula: see text], with [Formula: see text], and geometric multiplicity one, our goal in this paper is to find sufficient conditions for the family of vector fields such that the dynamics on the [Formula: see text]-dimensional [Formula: see text]-parameterized center manifold around the equilibrium point becomes locally topologically equivalent to a given unfolding. Finally, the result is applied to the study of the Rössler system.