Geodesic
A Special Ergodic Theorem for Anosov Diffeomorphisms on the 2-Torus
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 1, pp. 69-78

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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).
Mots-clés : Hausdorff dimension, Markov chain
Keywords: special ergodic theorem, Anosov diffeomorphism, large deviation theorem. 
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     author = {P. S. Saltykov},
     title = {A {Special} {Ergodic} {Theorem} for {Anosov} {Diffeomorphisms} on the {2-Torus}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2011_45_1_a5/}
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P. S. Saltykov. A Special Ergodic Theorem for Anosov Diffeomorphisms on the 2-Torus. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 1, pp. 69-78. http://geodesic.mathdoc.fr/item/FAA_2011_45_1_a5/