On Differentiability of Srb States for Partially Hyperbolic Systems
نویسنده
چکیده
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 if A is a C ∞ function then the map A → νε(A) is differentiable at ε = 0. This implies (Corollary 1) that the difference of Birkhoff averages of the perturbed and unperturbed systems is proportional to ε. We apply this result (Corollary 3) to show that if f0 is a time one map of geodesic flow on a unit tangent bundle over a surface of negative curvature then a generic perturbation has a unique SRB measure with good statistical properties.
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تاریخ انتشار 2006