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Igor Mezic, University of California at Santa Barbara – Ergodic Theory Seminar
April 14 @ 1:00 pm - 2:00 pm
Igor Mezic, University of California at Santa Barbara
Time: 1:00 pm Eastern Time Title: Ergodic theory and Koopman operator theory for dissipative systems Abstract: Classical Koopman operator theory provides a fruitful template for studies in ergodic theory of measure-preserving systems. It is of interest to extend its use to studies of dissipative systems – those that are globally attractive (in Birkhoff sense) to an invariant ergodic measure that is singular with respect to a predefined measure of interest (e.g. Lebesgue measure). The issue that arises is that of appropriate functional spaces to work in (pure L^2 theory has some issues), and we define these using an internal tensor product. As a consequence of the nature of the functional space, the spectrum of the operator is simplified. The extension also leads to new geometric objects related to state space partitions, such as isostables, and enables efficient analysis of physical models, but also of data. |