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manuscripta mathematica

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

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

  • Michael Reeken
Article

Abstract

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.

Keywords

Number Theory Small Perturbation Algebraic Geometry Topological Group Analytic Theory 
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References

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    MARTI, J.T.: Introduction to the theory of bases. Springer Verlag, Berlin Heidelberg New York 1969, p. 31, Theorem 4.Google Scholar
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    LANG, S.: Introduction to differentiable manifolds. John Wiley & Sons Inc. New York London 1962, p. 15, Corollary 2.Google Scholar
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    GOLDBERG, S.: Unbounded linear operators. Mac Grew-Hill Book Company 1966, p. 112, Theorem V. 1.6.Google Scholar
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    BÖHME, R.: Störungen der isolierten Eigenwerte selbstadjungierter Operatoren. Mathematische Zeitschrift, Band 123, Heft 1, 1971.Google Scholar
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    SCHWARTZ, J.T.: Nonlinear functional analysis. Lecture Notes 1965, Courant Institute of Mathematical Sciences New York University, p. 177.Google Scholar
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    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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