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Saturday, May 15

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IP7

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*