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Bifurcation from periodic solutions with spatiotemporal symmetry, including resonances and mode interactions

Lamb, JSW, Melbourne, I and Wulff, C (2003) Bifurcation from periodic solutions with spatiotemporal symmetry, including resonances and mode interactions JOURNAL OF DIFFERENTIAL EQUATIONS, 191 (2). 377 - 407. ISSN 0022-0396

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Abstract

We study local bifurcation in equivariant dynamical systems from periodic solutions with a mixture of spatial and spatiotemporal symmetries.

In previous work, we focused primarily on codimension one bifurcations. In this paper, we show that the techniques used in the codimension one analysis can be extended to understand also higher codimension bifurcations, including resonant bifurcations and mode interactions. In particular, we present a general reduction scheme by which we relate bifurcations from periodic solutions to bifurcations from fixed points of twisted equivariant diffeomorphisms, which in turn are linked via normal form theory to bifurcations from equilibria of equivariant vector fields.

We also obtain a general theory for bifurcation from relative periodic solutions and we show how to incorporate time-reversal symmetries into our framework.

Item Type: Article
Uncontrolled Keywords: Science & Technology, Physical Sciences, Mathematics, equivariant bifurcation theory, periodic and relative periodic solutions, spatiotemporal symmetry, mode interactions, RELATIVE EQUILIBRIA, ROTATING WAVES, SYSTEMS, ORBITS, DYNAMICS, FLOWS, MAPS
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Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:41
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1458

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