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Dynamics and geometry in forced symmetry breaking: a tetrahedral example

Published online by Cambridge University Press:  07 September 2004

DAVID CHILLINGWORTH  and
REINER LAUTERBACH
DAVID CHILLINGWORTH
Affiliation:
School of Mathematics, University of Southampton, Southampton, SO17 1 BJ. e-mail: D.R.J.Chillingworth@maths.soton.ac.uk
REINER LAUTERBACH
Affiliation:
Fachbereich Mathematik, Universität Hamburg, Bundesstraβe 55, 20146 Hamburg, Germany. e-mail: lauterbach@math.uni-hamburg.de
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Abstract

We are interested in the dynamics that can arise close to rotational group orbits after forced symmetry-breaking to discrete symmetries. In particular we ask how simple or complicated the dynamics induced by symmetric linear vector fields can be. We look in detail at related tetrahedral and dihedral examples, and there we find precise conditions for a linear field to exhibit homoclinic orbits.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 137 , Issue 2 , September 2004 , pp. 411 - 432
Copyright
2004 Cambridge Philosophical Society

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