Subharmonic bifurcation from relative equilibria in reversible systems with rotation symmetry

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.