Linear response formula for piecewise expanding unimodal maps

Preprint
Publisher Website
Google Scholar
Abstract
The average R(t) of a smooth function with respect to the SRB measure of a smooth one-parameter family f_t of piecewise expanding interval maps is not always Lipschitz. We prove that if f_t is tangent to the topological class of f_0, and if, then R(t) is differentiable at zero, and the derivative coincides with the resummation previously proposed by the first named author of the (a priori divergent) series given by Ruelle's conjecture. It is the first time that a linear response formula is obtained in a setting where structural stability does not hold.

This publication has 0 references indexed in Scilit: