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A systematic study of heteroclinic cycles in dynamical systems with broken symmetries

Published online by Cambridge University Press:  14 November 2011

Reiner Lauterbach ,
Stanislaus Maier-Paape  and
Ernst Reissner
Reiner Lauterbach
Affiliation:
Weierstrass Institut für angewandte Analysis und Stochastik, Mohrenstrasse 39, D-10117 Berlin, Germany
Stanislaus Maier-Paape
Affiliation:
Institut für Mathematik, Universität Augsburg, Universitätsstrasse 14, D-86135 Augsburg, Germany
Ernst Reissner
Affiliation:
Institut für Mathematik, Universität Augsburg, Universitätsstrasse 14, D-86135 Augsburg, Germany
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Abstract

Let X be a Banach space or a manifold and G a compact Lie group acting on X. We study G-equivariant (semi)flows on X in the context of forced symmetry breaking. After applying small symmetry breaking perturbations, certain generic invariant manifolds of the above flows persist slightly changed. We obtain necessary and sufficient conditions for the existence of heteroclinic cycles on the perturbed manifolds. Applications are given for the case G = SO(3).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 4 , 1996 , pp. 885 - 909
Copyright
Copyright © Royal Society of Edinburgh 1996

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