Preprint A45/2007
Linear response formula for piecewise expanding unimodal maps

Baladi, Viviane

**Keywords: **
linear response | unimodal maps | SRB measure

The average $R(t)=\int \varphi\, d\mu_t$ of a smooth
function $\varphi$ with respect to the SRB measure $\mu_t$
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 $f$ then $R(t)$ is differentiable at zero, and $R'(0)$
coincides with a resummation 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.