Linear response formula for piecewise expanding unimodal maps

Details Linear response formula for piecewise expanding unimodal maps Linear response formula for piecewise expanding unimodal maps

2007-05-23

arxiv.org/abs/0705.3383v3

Mathematics

Dynamical Systems

We added Theorem 7.1 which shows that the horizontality condition is necessary. The paper "Smooth deformations..." containing

Scientific paper

10.1088/0951-7715/21/4/003

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.

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