Linear response formula for piecewise expanding unimodal maps

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.

We added Theorem 7.1 which shows that the horizontality condition is necessary. The paper "Smooth deformations..." containing Thm 2.8 is now available on the arxiv; see also Corrigendum arXiv:1205.5468 (to appear Nonlinearity 2012)

References in corpus (5)

• On the susceptibility function of piecewise expanding interval maps
• Differentiating the absolutely continuous invariant measure of an interval map f with respect to f
• Smooth deformations of piecewise expanding unimodal maps
• Analyticity of the SRB measure of a lattice of coupled Anosov diffeomorphisms of the torus
• Structure and f-dependence of the a.c.i.m. for a unimodal map f of Misiurewicz type

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