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.
Citation:
P. S. Saltykov, “A Special Ergodic Theorem for Anosov Diffeomorphisms on the 2-Torus”, Funktsional. Anal. i Prilozhen., 45:1 (2011), 69–78; Funct. Anal. Appl., 45:1 (2011), 56–63