Pattern Formation in Continuous and Coupled Systems (M. Golubitsky, D. Luss and S. Strogatz, eds). IMA Volumes in Mathematics and its Applications 115, Springer, 1999, 175-191.
Jeroen Lamb and Ian Melbourne
Abstract
In this paper, we discuss some recent developments in the understanding of generic bifurcation from periodic solutions with spatiotemporal symmetries. We focus mainly on the theory for bifurcation from isolated periodic solutions in dynamical systems with a compact symmetry group.
Moreover, we discuss how our theory justifies certain heuristic assumptions underlying previous approaches towards period preserving and period doubling bifurcation from periodic solutions.