Limit theorems for self-similar tilings

Details Limit theorems for self-similar tilings Limit theorems for self-similar tilings

2012-01-30

arxiv.org/abs/1201.6092v1

Mathematics

Dynamical Systems

33 pages

Scientific paper

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.

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