Stability of critical points under small perturbations Part I: Topological theory

Abstract

We study the stability of critical points of a real valued C1 function f on a Finsler-manifold M under small perturbations of f. We give a topological description of certain (possibly degenerate) critical levels of f and show that for a certain class of functions g on M the function f+g has in a prescribed neighbourhood of the critical level of f a set of critical points the category of which is bounded below by an integer given by the topological description of that critical level of f. © 1972 Springer-Verlag.