How to get far with only a small effort

Job Candidate Talk
Tuesday, April 13, 2010 - 11:00
1 hour (actually 50 minutes)
Skiles 269
Department of Mathematics, University of Texas, Austin
Many mechanical systems have the property that some small perturbations can accumulate over time to lead to large effects. Other perturbations just average out and cancel. It is interesting in applications to find out what systems have these properties and which perturbations average out and which ones grows. A complete answer is far from known but it is known that it is complicated and that, for example, number theory plays a role. In recent times, there has been some progress understanding some mechanisms that lead to instability. One can find landmarks that organize the long term behavior and provide an skeleton for the dynamics. Some of these landmarks provide highways along which the perturbations can accumulate.