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Bifurcation from relative periodic solutions

Published online by Cambridge University Press:  30 March 2001

CLAUDIA WULFF ,
JEROEN S. W. LAMB  and
IAN MELBOURNE
CLAUDIA WULFF
Affiliation:
Institut für Mathematik I, Freie Universität Berlin, Arnimallee 2-6, 14195 Berlin, Germany
JEROEN S. W. LAMB
Affiliation:
Department of Mathematics, Imperial College, 180 Queens Gate, London SW7 2BZ, UK (e-mail: [email protected])
IAN MELBOURNE
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3476, USA
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Abstract

Relative periodic solutions are ubiquitous in dynamical systems with continuous symmetry. Recently, Sandstede, Scheel and Wulff derived a center bundle theorem, reducing local bifurcation from relative periodic solutions to a finite-dimensional problem. Independently, Lamb and Melbourne showed how to systematically study local bifurcation from isolated periodic solutions with discrete spatiotemporal symmetries.

In this paper, we show how the center bundle theorem, when combined with certain group theoretic results, reduces bifurcation from relative periodic solutions to bifurcation from isolated periodic solutions. In this way, we obtain a systematic approach to the study of local bifurcation from relative periodic solutions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 2 , April 2001 , pp. 605 - 635
Copyright
2001 Cambridge University Press

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