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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
BROWDER, F.: Existence theorems for nonlinear partial differential equations. Global Analysis Proceedings of symposia in pure mathematics XVL, 1–60, (1970).
FOX, R.H.: On the Lusternik-Shnirelman category. Annals of Mathematics42, (April 1941).
PALAIS, R.: Critical point theory and the minimax principle. Global Analysis. Proceedings of symposia in pure mathematics XV, 185–212, (1970).
Author information
Authors and Affiliations
Additional information
This work was supported by Grant No. 2.464.71 of the F.N.S.R.S.
Rights and permissions
About this article
Cite this article
Reeken, M. Stability of critical points under small perturbations Part I: Topological theory. Manuscripta Math 7, 387–411 (1972). https://doi.org/10.1007/BF01644075
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01644075