Ian Melbourne
Department of Mathematics, University of Surrey, U.K.
Corkscrews and boomerang-like motions
Wednesday 29th November 14:05-14:55pm,
Carslaw Building Room 373.
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.