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manuscripta mathematica

, Volume 7, Issue 4, pp 387–411 | Cite as

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

  • Michael Reeken
Article

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.

Keywords

Number Theory Small Perturbation Algebraic Geometry Critical Level Topological Group 
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References

  1. [1]
    BROWDER, F.: Existence theorems for nonlinear partial differential equations. Global Analysis Proceedings of symposia in pure mathematics XVL, 1–60, (1970).Google Scholar
  2. [2]
    FOX, R.H.: On the Lusternik-Shnirelman category. Annals of Mathematics42, (April 1941).Google Scholar
  3. [3]
    PALAIS, R.: Critical point theory and the minimax principle. Global Analysis. Proceedings of symposia in pure mathematics XV, 185–212, (1970).Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • Michael Reeken
    • 1
  1. 1.Advanced Studies CenterBattelle InstituteCarouge-Geneva

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