Devroye Inequality for a Class of Non - Uniformly Hyperbolic Dynamical Systems
نویسنده
چکیده
In this paper, we prove an inequality, which we call " Devroye inequality " , for a large class of non-uniformly hyperbolic dynamical systems (M, f). This class, introduced by L.-S. Young, includes families of piece-wise hyperbolic maps (Lozi-like maps), scattering billiards (e.g., planar Lorentz gas), unimodal and Hénon-like maps. Devroye inequality provides an upper bound for the variance of observables of the form K(x, f (x),. .. , f n−1 (x)), where K is any separately Hölder continuous function of n variables. In particular, we can deal with observables which are not Birkhoff averages. We will show in [2] some applications of Devroye inequality to statistical properties of this class of dynamical systems.
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