DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Suddhasattwa Das, University of Maryland

**Title: ***
A Low Dimensional Paradigm for High Dimensional Chaos
*

**Abstract:**
Chaotic systems are characterized by sensitive dependence on initial conditions, dense trajectories and dense periodic points. Usually, embedded periodic orbits in the chaotic sets that are studied have the same number of unstable dimensions, but this property seems to fail in high dimensional systems. In this talk, I will define a property called multi-chaos, in which there are dense periodic orbits of more than one unstable dimension, along with the usual properties of chaos. We construct a family of toral maps which happen to be the first example of multi-chaos. These form a broad class of maps on the torus and and we exhibit a mechanism under which multi-chaos occurs. One of the key features of these maps is the presence of an invariant structure called a "expanding, invariant cone system".

**Time:** Friday, December 11, 2015, 1:30-2:30 p.m.

**Place:** Exploratory Hall, 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