Speaker:Jay Mireles James, Rutgers University
Title: Computer assisted proof of connecting orbits in dynamical systems by the projected boundary approach

Abstract: Understanding heteroclinic connections between equilibria and periodic orbits is a step toward understanding the global dynamics of a nonlinear dynamical system. For smooth dynamical systems these connections arise as intersections of stable and unstable manifolds. I will discuss some computational tools for studying stable and unstable manifolds of equilibria and periodic orbits of differential equations, as well as some methods for computing transverse intersections between these manifolds. The methods are based on reformulating the manifolds and connecting orbits as solutions of certain operator equations. A-posteriori error analysis for these operator equations leads to methods of computer assisted proof. I will try to pepper the discussion with example results.

Time: Friday, November 8, 2013, 1:30-2:30 p.m.

Place: Exploratory Hall (formerly S & T II), Room 4106

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