Stochastic Behavior in Deterministic Dynamical Systems

2:00 PM-2:45 PM

*Room: Capitol Center/South*

*Chair: Fan Chung Graham, University of Pennsylvania*

By a deterministic dynamical system, we refer to a system generated by an iterative scheme or by an ordinary differential equation. In this lecture, we ask to what degree observations from deterministic dynamical systems can resemble those from (genuinely random) stochastic processes (such as flipping a coin). We discuss statistical properties including asymptotic distributions of orbits, the central limit theorem, and rates of correlation decay and explain recent rigorous results in nontechnical language. We illustrate the relation between the geometry of the map and the statistical properties of the observed data by example.

**Lai-Sang Young**

*Department of Mathematics, University of California, Los Angeles;
and Courant Institute of Mathematical Sciences, New York University*

*MMD, 2/2/99*