Giovanni Canestrari (Università di Bologna) and Wael Bahsoun (Loughborough University)

Abstract: In this talk we will introduce the mathematical objects in the linear response theory of chaotic dynamical systems. We will discuss how such theories try to give an explanation of some physical phenomena and, after that, we will give an introduction to a rigorous linear response calculation. Finally, we will discuss obstacles to linear response and recent challenges in the mathematical literature.

Abstract: It is well known that a family of tent maps with bounded derivatives has no linear response (the absolutely continuous invariant measure is not differentiable with respect to perturbation) for typical deterministic perturbations changing the value of the turning point. In this talk we consider a tent-like family with a cusp at the turning point and show that for such a family we recover the linear response. This is a joint work with S. Galatolo. At the end of the talk I will also mention briefly new results by Canestrari about linear response for systems with discontinuities in higher dimensions.