Where: Kirwan Hall 0301

Speaker: Alex Blumenthal (UMD) -

Abstract: Hyperbolicity is the infinitesimal dynamical mechanism responsible for chaotic behavior of trajectories x_n, n \geq 0. Hyperbolic systems tend to have the property that for Holder regular observables \phi, the time-n observations \phi(x_n) tend to behave like weakly correlated random variables and satisfy (i) fast decay of correlations and (ii) a central limit theorem (the latter only for "typical" observables). In my two talks at the stochastics RIT, I will prove properties (i) and (ii) in the slightly simpler setting of uniformly expanding maps, describing briefly how these ideas pertain to uniformly hyperbolic systems.

Where: Kirwan Hall 0301

Speaker: Jacob Bedrossian (UMD) -

Abstract: We will discuss the 1989 paper of the same name by Baxendale.

Where: Kirwan Hall 0301

Speaker: Jacob Bedrossian (UMD) -

Abstract: Continuation of discussion of Baxendale's 1989 paper of the same name

Where: Kirwan Hall 0301

Speaker: Mark Freidlin (UMD) -

Abstract: I will present a general approach to various asymptotic problems concerning long time influence of small deterministic or stochastic perturbations of dynamical systems, semi-flows defined by evolutionary PDEs, and diffusion processes. Long time evolution of the perturbed system can be described by a motion on the

simplex M of invariant probability measures of the non-perturbed system. The

simplex is, in a sefanse, an analogy to the action coordinates for completely

integrable Hamiltonian systems, and the measure corresponding to a point of the simplex M characterizes the generalized action coordinates.

As examples of such an approach, regularized averaging principle, random

perturbations of systems with asymptotically stable attractors, wave fronts in

Reaction-Diffusion Equations, homogenization problems, and some other

asymptotic problems for PDEs will be considered.

The limiting motion on the simplex M, in an appropriate time scale, is determined

by laws of large numbers, diffusion approximation, or by the limit theorems for

large deviations.

Where: 0301

Speaker: Sandra Cerrai (UMD) -

Where: 0301

Speaker: Mark Freidlin (UMD) -

Abstract: I will present a general approach to various asymptotic problems concerning long time influence of small deterministic or stochastic perturbations of dynamical systems, semi-flows defined by evolutionary PDEs, and diffusion processes. Long time evolution of the perturbed system can be described by a motion on the simplex M of invariant probability measures of the non-perturbed system. The simplex is, in a sense, an analogy to the action coordinates for completely integrable Hamiltonian systems, and the measure corresponding to a point of the simplex M characterizes the generalized action coordinates.

As examples of such an approach, regularized averaging principle, random

perturbations of systems with asymptotically stable attractors, wave fronts in

Reaction-Diffusion Equations, homogenization problems, and some other

asymptotic problems for PDEs will be considered. The limiting motion on the simplex M, in an appropriate time scale, is determined by laws of large numbers, diffusion approximation, or by the limit theorems for large deviations.