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Catastrophes and Bifurcations in Variational Problems

  • G. Dangelmayr
Part of the Springer Series in Synergetics book series (SSSYN, volume 4)

Summary

Using an extension of catastrophe theory to infinite dimensional spaces, the bifurcation properties of the solutions of nonlinear operator equations, deriving from variational problems, are shown to be determined by those of the stationary points of unfoldings of singularities and so are classifiable in terms of catastrophe polynomials. A stability analysis of the bifurcating solutions is carried out. The results are applied to the buckling of columns and lead here to a nonversal unfolding of a double-cusp. Implications of the techniques for nonequilibrium thermodynamics are indicated.

Keywords

Stationary Point Variational Problem Bifurcation Diagram Catastrophe Theory Reflexive Banach Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • G. Dangelmayr
    • 1
  1. 1.Institute for Information SciencesUniversity of TübingenTübingenFed. Rep. of Germany

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