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The G-invariant implicit function theorem in infinite dimensions

Published online by Cambridge University Press:  14 November 2011

E. N. Dancer
E. N. Dancer
Affiliation:
Department of Mathematics, University of New England, Armidale, N.S.W. 2351, Australia
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Synopsis

Our basic theorem is a version of the implicit function theorem in the case of continuous groups of symmetries. The result is sufficiently general to cover a great many applications. It generalizes some earlier work of the author and corrects and improves some work of Vanderbauwhede. We also consider the breaking of symmetries problem and the variational case. Finally, we apply our results to study the periodic solutions of an ordinary differential equation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 1-2 , 1982 , pp. 13 - 30
Copyright
Copyright © Royal Society of Edinburgh 1982

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