Type: Seminar

Distribution: World

Expiry: 29 Nov 2006

Auth: gottwald@p6363.pc.maths.usyd.edu.au

I will describe recent work by PhD student David Chan on dynamical systems with symmetry group E(3) -- rotations and translations in 3-D space. This is the 3-D counterpart to Barkley’s work on the transition from meandering to linear drifting spirals in planar systems. The simplest dynamics (relative equilibrium) is a rigid corkscrew motion. Hopf bifurcation (or periodic forcing) typically induces a periodic oscillation of the underlying corkscrew. The resonant case is much more interesting and quite surprising. This occurs when the frequency of rotation around the original corkscrew is an integer multiple of the Hopf/forcing frequency. Chan shows that resonant Hopf bifurcation (a codimension two phenomenon) leads to a boomerang-like motion.