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Groups And Dynamics
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Alex Blumenthal, RLM 8.136: The Multiplicative Ergodic Theorem: Background, Applications and Extensions
Tuesday, March 12, 2019, 10:00am - 11:00am
The Multiplicative Ergodic Theorem (MET), originally due to Oseledetsin the 1960s, describes the asymptotic exponential growth ratesof vectors under products of stationary sequences of matrices.When applied to the derivative of a smooth dynamical system,the MET can be used to describe the asymptotic exponential ratesof separation/attraction of nearby trajectories at the infinitesimallevel. This observation forms the basis for Pesin theory, a generalizedtheory of stable/unstable manifolds, which today underpins alarge proportion of studies in smooth ergodic theory. In thistalk I will formulate and discuss the MET, discuss some of itsmany applications, and describe how this result generalizes tothe setting of compositions of stationary sequences of operatorson an infinite-dimensional Banach space.
Location: RLM 8.136

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