manuscripta mathematica

, Volume 8, Issue 1, pp 69–92 | Cite as

Stability of critical points under small perturbations part II: Analytic theory

  • Michael Reeken


We prove a global version of the implicit function theorem in the sense that instead of having a parameter dependent point as solution we have a parameter dependent manifold. With the help of this we continue the study of bifurcation for gradient systems which we began in part I with topological methods.


Number Theory Small Perturbation Algebraic Geometry Topological Group Analytic Theory 
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  1. [4]
    MARTI, J.T.: Introduction to the theory of bases. Springer Verlag, Berlin Heidelberg New York 1969, p. 31, Theorem 4.Google Scholar
  2. [5]
    LANG, S.: Introduction to differentiable manifolds. John Wiley & Sons Inc. New York London 1962, p. 15, Corollary 2.Google Scholar
  3. [6]
    GOLDBERG, S.: Unbounded linear operators. Mac Grew-Hill Book Company 1966, p. 112, Theorem V. 1.6.Google Scholar
  4. [7]
    BÖHME, R.: Störungen der isolierten Eigenwerte selbstadjungierter Operatoren. Mathematische Zeitschrift, Band 123, Heft 1, 1971.Google Scholar
  5. [8]
    SCHWARTZ, J.T.: Nonlinear functional analysis. Lecture Notes 1965, Courant Institute of Mathematical Sciences New York University, p. 177.Google Scholar
  6. [9]
    PALAIS R.: Morse theory on Hilbert manifolds. Topology Vol. 2, 1963, p. 335.Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

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

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