DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** William Ott, Mathematics, University of Houston

**Title: ***
Searching for SRB measures
*

**Abstract:**
Dynamical systems with hyperbolic properties display sensitive dependence on initial conditions: trajectories that start close together quickly move apart. We therefore adopt a statistical viewpoint. Does there exist an invariant measure that describes the asymptotic distribution of a typical orbit? For dissipative dynamical systems, Sinai/Ruelle/Bowen (SRB) measures do so. They are associated with chaotic motion that is both sustained in time (positive Lyapunov exponent(s)) and physically observable.

In this talk I will describe recent work on proving the existence of SRB measures in concrete systems of interest in the physical and biological sciences. The idea is the following. Start with a flow with some type of intrinsic shear or twist. If such a flow is gently forced, the forcing may amplify the shear and thereby produce nonuniform hyperbolicity and SRB measures. Shear arises naturally near homoclinic loops and limit cycles. We discuss both settings in the context of finite-dimensional flows and the latter in the context of reaction diffusion PDEs.

**Time:** Friday, Apr. 1, 2011, 1:30-2:30 p.m.

**Place:** Science and Tech I, Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491