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VOL. 53 | 2009 Subharmonic bifurcation from relative equilibria in reversible systems with rotation symmetry
André Vanderbauwhede

Editor(s) Saber Elaydi, Kazuo Nishimura, Mitsuhiro Shishikura, Nobuyuki Tose

## Abstract

In this paper we study the bifurcation of subharmonic tori from branches of symmetric relative equilibria in reversible systems with an additional $S^1$-symmetry. The analysis is based on a detailed study of the Poincaré map, which appears to be generated by a reduced vectorfield on the section. The results are applied to a simple example system, but the bifurcation behaviour described by our theoretical results can also be observed in, for example, the spherical pendulum and the Furuta pendulum.

## Information

Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1192.37075
MathSciNet: MR2582434

Digital Object Identifier: 10.2969/aspm/05310371