Title: Brownian motion in deterministic dynamical systems with Euclidean symmetry
Speaker: Prof. Ian Melbourne
Speaker Info: University of Houston
Spirals in chemical reactions exhibit a behavior known as `hypermeander', where the motion of the spiral tip resembles a Brownian motion. Biktashev and Holden proposed that this is a consequence of Euclidean symmetry and deterministic chaos.Date: Friday, January 28, 2000
Motivated by these observations, we prove rigorous results on the dynamics associated with chaotic attractors for dynamical systems with noncompact symmetry group. Under hyperbolicity assumptions on the attractor and assumptions on the symmetry group, we show that generically the asymptotic dynamics resembles a Brownian motion. In the case of Euclidean E(n) symmetry, we have positive results so far for the cases n=2 and n odd.
A consequence of our work is an explanation/prediction of hypermeander of spirals in chemical reactions.
This is joint work with Peter Ashwin and Matthew Nicol.