Probabilistic chaos: history, recent developments, and future prospects

4:00 pm Thursday, September 24, 2009
William Ott (University of Houston)


It is often difficult or impossible to determine if a specific dynamical system possesses chaotic properties. It is therefore natural to study parametrized families of dynamical systems and focus on how the dynamics vary with the parameters. Probabilistic chaos occurs when chaotic phenomena are present for a set of parameters of positive Lebesgue measure. In this talk we first examine the major mathematical developments, from the foundational theorem of Jakobson to the recent theory of rank one maps developed by Wang and Young. We then discuss applications of the theory of rank one maps to concrete systems. Finally, we speculate about the role that probabilistic chaos will play in the analysis of infinite-dimensional systems arising from partial differential equations.

 

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