Ergodic Theory and Dynamical Systems



Bifurcation from relative periodic solutions


CLAUDIA WULFF a1, JEROEN S. W. LAMB a2 and IAN MELBOURNE a3
a1 Institut für Mathematik I, Freie Universität Berlin, Arnimallee 2-6, 14195 Berlin, Germany
a2 Department of Mathematics, Imperial College, 180 Queens Gate, London SW7 2BZ, UK (e-mail: jsw.lamb@ic.ac.uk)
a3 Department of Mathematics, University of Houston, Houston, TX 77204-3476, USA

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.

(Received April 20 1999)
(Revised December 1 1999)