Linear response formula for piecewise expanding unimodal maps
Dynamical Systems
2012-05-28 v3
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, 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.
Cite
@article{arxiv.0705.3383,
title = {Linear response formula for piecewise expanding unimodal maps},
author = {V. Baladi and D. Smania},
journal= {arXiv preprint arXiv:0705.3383},
year = {2012}
}