Lamb, Jeroen S. W., Melbourne, I. and Wulff, C. (2003) Bifurcation from periodic solutions with spatiotemporal symmetry, including resonances and mode interactions. Journal of Differential Equations, 191 (2). pp. 377-407. doi:10.1016/S0022-0396(03)00019-6

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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. © 2003 Elsevier Science (USA). All rights reserved.

Item Type:	Journal Article
Subjects:	R Medicine > R Medicine (General)
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Journal of Differential Equations
Publisher:	Academic Press
ISSN:	0022-0396
Official Date:	1 July 2003
Dates:	Date Event 1 July 2003 Published
Date of first compliant deposit:	26 July 2018
Volume:	191
Number:	2
Page Range:	pp. 377-407
DOI:	10.1016/S0022-0396(03)00019-6
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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