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. © 2012 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Bufetov, A. I., & Solomyak, B. (2013). Limit Theorems for Self-Similar Tilings. Communications in Mathematical Physics, 319(3), 761–789. https://doi.org/10.1007/s00220-012-1624-7
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