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Automating Symmetry-Breaking Calculations

Published online by Cambridge University Press:  01 February 2010

P. C. Matthews
P. C. Matthews
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom, paul.matthews@nottingham.ac.uk, http://www.maths.nottingham.ac.uk/personal/pcm

Abstract

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The process of classifying possible symmetry-breaking bifurcations requires a computation involving the subgroups and irreducible representations of the original symmetry group. It is shown how this calculation can be automated using a group theory package such as GAP. This enables a number of new results to be obtained for larger symmetry groups, where manual computation is impractical. Examples of symmetric and alternating groups are given, and the method is also applied to the spatial symmetry-breaking of periodic patterns observed in experiments.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 7 , 2004 , pp. 101 - 119
Copyright
Copyright © London Mathematical Society 2004

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