DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** Jim Yorke, Mathematics, University of Maryland

**Title: ***
Period-doubling Cascades galore - explaining a phenomenon we see in dynamical systems
*

**Abstract:**
The presence of period-doubling cascades in dynamical systems
depending on one parameter is a hallmark of the onset of highly
complex dynamics. However, their existence has only been explained in
a quite restrictive set of examples. A general cascade involves a
limit of closely spaced period-doubling points which may not be attracting. Cascades are
therefore difficult to find computationally in all but simple cases. Our theoretical techniques
allow us to explain why cascades occur, as well as to verify that
there are infinitely many different cascades. We are also
able to use our geometric methods to give precise bounds on the number
of cascades of a given period.
This is joint work with Evelyn Sander, based on prior joint work with Kathleen Alligood.

**Time:** Friday, November 7, 2008, 1:30-2:30 p.m.

**Place:** Science and technology 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