Long Time Effect of Small Perturbations

Tuesday, January 15, 2013 - 11:30am - 12:20pm
Keller 3-180
Mark Freidlin (University of Maryland)
I will consider long time influence of small deterministic and stochastic perturbations of various dynamical systems
and stochastic processes. The long time evolution of the perturbed system can be described by a motion in the cone
of invariant measures of the non-perturbed system. The set of extreme points of the cone can be often parametrized
by a graph or by an open book. The slow component of the perturbed system, is a process on this object.

I will demonstrate how this general approach works in the case of perturbations of systems with several asymptotically stable attractors, perturbations of an oscillator, of elastic systems, of the Landau-Lifshitz equation and its generalization. The same approach works also when PDEs with a small parameter are considered: the Neumann problem with a small parameter for second order elliptic PDEs will be considered.
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