## Transitions from relative equilibria to relative periodic orbits

### Summary

Summary: We consider $G$-equivariant semilinear parabolic equations where $G$ is a finite-dimensional possibly non-compact symmetry group. We treat periodic forcing of relative equilibria and resonant periodic forcing of relative periodic orbits as well as Hopf bifurcation from relative equilibria to relative periodic orbits using Lyapunov-Schmidt reduction. Our main interest are drift phenomena caused by resonance. In comparison to a center manifold approach Lyapunov-Schmidt reduction is technically easier. We discuss impacts of our results on spiral wave dynamics.

### Mathematics Subject Classification

35B32, 35K57, 57S20

### Keywords/Phrases

spiral waves, equivariant dynamical systems, noncompact groups