# On differentiability of SRB states for partially hyperbolic systems

@article{Dolgopyat2004OnDO, title={On differentiability of SRB states for partially hyperbolic systems}, author={Dmitry Dolgopyat}, journal={Inventiones mathematicae}, year={2004}, volume={155}, pages={389-449} }

Consider a one parameter family of diffeomorphisms fε such that f0 is an Anosov element in a standard abelian Anosov action having sufficiently strong mixing properties. Let νε be any u-Gibbs state for fε. We prove (Theorem 1) that for any C∞ function A the map ε→νε(A) is differentiable at ε=0. This implies (Corollary 2.2) that the difference of Birkhoff averages of the perturbed and unperturbed systems is proportional to ε. We apply this result (Corollary 3.3) to show that a generic…

## 129 Citations

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