Abstract

Jeroen S. W. Lamb, Ian Melbourne, Claudia Wulff.

Hopf Bifurcation from Relative Periodic Solutions; Secondary Bifurcations from Meandering Spirals

We consider nonresonant and weakly resonant Hopf bifurcation from periodic solutions and relative periodic solutions in dynamical systems with symmetry. In particular, we analyse phase-locking and irrational torus flows on the bifurcating relative tori. Results are obtained for systems with compact and noncompact symmetry group. In the noncompact case, we distinguish between bounded and unbounded dynamics. Applications of our results include secondary Hopf bifurcation from meandering multi-armed spirals.