Mathematics Colloquia and Seminars

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We will consider discrete-time dynamical systems generated by the convolution of the heat kernel with a Koopman operator, given by an arbitrary measure preserving transformation on d-dimensional torus. Such dynamical systems arises from the study of long time transport property of a fluid particle in the case of periodic, divergence free velocity field and subject to the white noise perturbation caused by molecular diffusion. We will define and describe the notion of the dissipation time of operators generating such systems and compute it explicitly for certain toral automorphism. In particular we'll classify all measurable automorphisms of the 2-dim torus according to their dissipation time. If time permits we will briefly discuss open questions and possibility of further generalizations of these results.