Dynamics and geometry in forced symmetry breaking: a tetrahedral example

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...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 2004-09, Vol.137 (2), p.411-432
Main Authors: CHILLINGWORTH, DAVID, LAUTERBACH, REINER
Format: Article
Language:English
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Summary: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.
ISSN:0305-0041
1469-8064
DOI:10.1017/S030500410400773X