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Minicourse: Spectral analysis of measurable dynamical systems.
Minicourse: Spectral analysis of measurable dynamical systems. Christopher Bose, University of Victoria, Canada. August 13-15, 2013.
CIMAT, Guanajuato, México
José Ángel Canavati Auditorium, CIMAT
* Lecture 1: Introduction to spectral analysis in ergodic theory. Transfer operators and associated spectral properties for invertible, measurepreserving dynamical systems. Spectral characterization of ergodicity, mixing and other levels in the dynamical hierarchy. Von Neumann's theorem and the discrete spectrum theorem as examples.
* Lecture 2: The theory for non-invertible, non-measure-preserving maps. The transfer operator for nonsingular systems. Quasi-compactness and dynamical consequences. The dynamical Perron-Frobenius theorem.
* Lecture 3: Spectral theory for expanding maps; theoretical and practical applications. The Lasota-Yorke inequality, quasi-compactness and a prelude to computational ergodic theory; Ulam's method as an example.
as well as specialized talks by researches and students.
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