Speaker: Sarah Day, College of William and Mary
Title: Computer-assisted proofs in dynamical systems
Abstract: With recent advances in computing power, numerical studies of nonlinear dynamical systems have become increasing more popular. However, errors inherent to such studies may obscure the dynamics or, in the very least, raise doubts about the existence of numerically observed structures. Furthermore, unstable behavior, an intrinsic element of complicated systems, may be difficult to track even with very careful numerical work. I will discuss topological techniques which allow for the rigorous detection of dynamical structures of various stability types. Towards the end of the talk, I will focus on recent work on expanding these techniques that led to the computation of a rigorous lower bound on the topological entropy (one measurement of complexity) for the (chaotic) Henon map.
Time: Friday, February 8, 2008, 3:30-4:20 p.m.Place: Science and Technology Building I, Room 242
Refreshments will be served before the talk at 3:00 p.m. in Room 222.
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