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Imperfect bifurcation and Banach space singularity theory

Part of: Calculus on manifolds; nonlinear operators

Published online by Cambridge University Press:  09 April 2009

Leif Arkeryd
Leif Arkeryd
Affiliation:
Department of Mathematics, Chalmers University of Technology, and The University of Göteborg, S-412 96 Göteborg, Sweden
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Abstract

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This paper generalizes the theory of imperfect bifurcation via singularity theory as developed by M. Golubitsky and D. Schaeffer to a Banach space setting. Like the parameter-free potential catastrophe theory, where similar generalizations have been discussed in the literature, Banach control spaces allow useful uniform control of function parameters through the universal unfolding. Among the results are tests for various germ properties and discussion of their reducibility under a Liapunov—Schmidt type splitting, as well as a generalization of the finite dimensional unfolding and germ classification theory.

Keywords

Bifurcation theory, imperfections, singularity theory, elementary catastrophes, versal unfolding, stable unfolding, reducible properties.

MSC classification

Secondary: 58C25: Differentiable maps
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 3 , October 1981 , pp. 294 - 311
Copyright
Copyright © Australian Mathematical Society 1981

References

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