Equadiff 99, International Conference on Differential Equations , (B. Fiedler et al. eds.) World Scientific, Singapore, 2000, 145-150.
Peter Ashwin, Ian Melbourne and Matthew Nicol
Abstract
We consider the behaviour of generic special Euclidean (SE(n)) group extensions of dynamical systems that are chaotic or quasiperiodic. Results of Nicol, Melbourne and Ashwin show that for a generic extension of a chaotic base dynamics, one will see a Brownian-like random walk if n>1 is odd or if n=2. For SE(2)-extensions of quasiperiodic dynamics, there is bounded motion for almost all smooth enough extensions.