Parameter regularity of dynamical determinants of expanding maps of the circle and an application to linear response

Abstract

In order to adapt to the differentiable setting a formula for linear response proved by Pollicott and Vytnova in the analytic setting, we show a result of regularity of dynamical determinants of expanding maps of the circle. The main tool is the decomposition of a transfer operator as a sum of a nuclear part and a "small" bounded part.

Quadratic response and speed of convergence of invariant measures in the zero-noise limit

“…In the paper [20], a relatively simple and quite general approach to the first and second order terms in the response of a system to perturbations is proposed and applied to deterministic perturbations of deterministic systems and perturbations of random systems (other approaches to higher order response can be found e.g. in [22,21,29,31,30]). In Subsection 2.1 we recall the main general results of [20].…”