This article is cited in 6 papers

A Special Ergodic Theorem for Anosov Diffeomorphisms on the 2-Torus

P. S. Saltykov

Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A strengthened version of the Birkhoff ergodic theorem for linear Anosov diffeomorphisms on the 2-torus is presented. Namely, it is proved that the Hausdorff dimension of the set of points at which partial limits of the time average strongly (by a constant) differ from the space average is strictly less than the dimension of the space (i.e., than 2).

Keywords: Hausdorff dimension, special ergodic theorem, Anosov diffeomorphism, Markov chain, large deviation theorem.

UDC: 517.987.5

Received: 09.11.2009

DOI: 10.4213/faa3028

 English version: Functional Analysis and Its Applications, 2011, 45:1, 56–63

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