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Statistical features of hyperbolic dynamical systems

4:00 pm Thursday, November 18, 2010
Matthew Nicol (University of Houston)

What can be said about the statistical properties of time-series arising from observations on a hyperbolic dynamical system? If the system is ergodic then the time-average is equal to the mean of the observation on the system. We discuss recent work on more refined statistical properties such as large deviations, extreme values and return time statistics. These results suggest that a slight amount of hyperbolicity entails that time-series of observations have the same limit laws as independent identically distributed (i.i.d) random variables. We will focus on key models such as unimodal maps and billiard systems.
The talk will be accessible to first year graduate students.

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