Alexander I. Bufetov, Boris Solomyak
Published 2012-01-30, updated 2012-04-27Version 2
We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic formula is given for ergodic integrals in terms of these finitely-additive measures, and, as a corollary, limit theorems are obtained for dynamical systems given by self-similar tilings.
Comments: 36 pages; some corrections and improved exposition, especially in Section 4; references added
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