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The classification of bifurcations with hidden symmetries
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Manoel, Míriam and Stewart, Ian, 1945. (2000) The classification of bifurcations with hidden symmetries. Proceedings of the London Mathematical Society , Vol.80 (No.1). pp. 198234. ISSN 00246115

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Official URL: http://dx.doi.org/10.1112/S0024611500012156
Abstract
We set up a singularitytheoretic framework for classifying oneparameter steadystate bifurcations with hidden symmetries. This framework also permits a nontrivial linearization at the bifurcation point. Many problems can be reduced to this situation; for instance, the bifurcation of steady or periodic solutions to certain elliptic partial differential equations with Neumann or Dirichlet boundary conditions. We formulate an appropriate equivalence relation with its associated tangent spaces, so that the usual methods of singularity theory become applicable. We also present an alternative method for computing those matrixvalued germs that appear in the equivalence relations employed in the classification of equivariant bifurcation problems. This result is motivated by hidden symmetries appearing in a class of partial differential equations defined on an Ndimensional rectangle under Neumann boundary conditions.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Mathematics 
Library of Congress Subject Headings (LCSH):  Bifurcation theory, Differential equations, Nonlinear  Numerical solutions, Singularities (Mathematics), Geometry, Algebraic, Manifolds (Mathematics), Symmetry (Mathematics) 
Journal or Publication Title:  Proceedings of the London Mathematical Society 
Publisher:  Cambridge University Press 
ISSN:  00246115 
Official Date:  January 2000 
Volume:  Vol.80 
Number:  No.1 
Page Range:  pp. 198234 
Identification Number:  10.1112/S0024611500012156 
Status:  Peer Reviewed 
Access rights to Published version:  Open Access 
References:  1. R. Abraham, J. E. Marsden and T. Ratiu, Manifolds, tensor analysis and applications (AddisonWesley, Reading, MA, 1983). 
URI:  http://wrap.warwick.ac.uk/id/eprint/836 
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