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arXiv · 0705.3383

Linear response formula for piecewise expanding unimodal maps

V. Baladi·D. Smania
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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.

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V. Baladi, D. Smania. 2007-10-19. Linear response formula for piecewise expanding unimodal maps. https://doi.org/10.1088/0951-7715%2F21%2F4%2F003

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