DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**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