Seminar by Stefano Galatolo: "Linear Response and Control of the Statistical Properties of Dynamics"

Stefano Galatolo, Associate Professor, Universita di Pisa, Italy

Abstract

The concept of linear response of a dynamical system describes how the invariant measure and then the statistical properties of the system change when a certain "infinitesimal" perturbation is applied to the system. This concept has important relations with the study of climate models and climate change. One inverse problem associated with linear response is the optimal response, which finds the best infinitesimal perturbation in order to modify the statistical properties of the system in some wanted direction.
One way to formalize the problem is by considering a given observable and searching for the optimal perturbation in order to maximize the average of the observable. The existence of an optimal solution has been proved in some classes of deterministic and random systems and numerical methods for its approximation have been shown. In the talk, we discuss the mathematical structure of the problem and review some recent results on the control of the statistical properties of random dynamical systems, expanding maps, hyperbolic deterministic systems. 

This seminar will be held in English.