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