DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** David Richeson, Mathematics, Dickinson College

**Title: ***
Obtaining entropy bounds for nonhyperbolic dynamical systems via symbolic dynamics
*

**Abstract:** We introduce index systems, a tool for studying
isolated invariant sets of dynamical systems that are not necessarily
hyperbolic. Every continuous dynamical system satisfying a weak form
of expansiveness possesses an index system. The mapping of the index
system mimics the expansion and contraction of hyperbolic maps on the
tangent space and they may be used like Markov partitions to generate
symbolic dynamics. However, because the elements of an index system
may have nontrivial intersections, itineraries are not necessarily
unique. Thus we conclude by discussing how to obtain entropy bounds
from symbolic dynamics generated from partitions with overlapping
elements.

**Time:** Friday, Jan. 28, 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