Title: Weak and Not so weak Mean Field Coupling regime. Invariant Measures, Convergence to Equilibrium, Linear Response
Abstract: We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems subjected to a mean field coupling. We consider a large class of self consistent transfer operators and prove general statements about existence of invariant measures, speed of convergence to equilibrium, statistical stability and linear response. We also consider the problem of finding the optimal coupling between maps in order to change the statistical properties of the system in a prescribed way.
Bio: Stefano Galatolo is Associate Professor at Dipartimento di Matematica, University of Pisa and director of Centro Interdipartimentale per lo Studio dei Sistemi Complessi. His research focuses on dynamical systems, its statistical behavior and computational methods. He is author of about 50 papers in these fields and currently editor of Chaos Solitons and Fractals and Journal of Fixed Point Theory and Applications.
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