Seminari di Sistemi Dinamici Olomorfi 2017-2018

# seminar: An implicit function approach to linear response

speaker: Julien Sedro (Université Paris-Sud)

abstract: Consider a family of dynamical systems $(ft){t\in-\epsilon,\epsilon}$ acting on some space M and depending smoothly on $t$, such that for each t there is a physical invariant measure $\mut$. We say that linear response holds if for an observable $\phi:M\rightarrow R$, the map $t\mapsto E{\mut}\phi$ has a derivative at t=0.

In this talk, we will present a new way of establishing linear response, through an implicit function approach. After briefly exposing the different existing ways to establish it, and the technical difficulties going with it, we will explain our approach, and how it brings together the 2 main methods : weak spectral perturbation à la Gouëzel-Keller-Liverani and quantitative fixed point stability.

We will illustrate the method on a simple model of chaotic dynamics, namely uniformly expanding maps of the d-dimensional torus. If time allows, we will also discuss higher-order response ,and the study of regularity of thermodynamical quantities of interest (topological pressureentropy, equilibrium states, variance in the central limit theorem...)

timetable:
Thu 8 Feb, 16:15 - 17:15, Sala Conferenze Centro De Giorgi
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