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Communications in Mathematical Physics

, Volume 319, Issue 3, pp 761–789 | Cite as

Limit Theorems for Self-Similar Tilings

  • Alexander I. Bufetov
  • Boris Solomyak
Article

Abstract

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.

Keywords

Limit Theorem Lipschitz Domain Substitution Matrix Translation Surface Ergodic Average 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Laboratoire d’Analyse, Topologie, Probabilités, Aix-Marseille Université, CNRSMarseilleFrance
  2. 2.Steklov InstituteMoscowRussia
  3. 3.The Institute for Information Transmission ProblemsMoscowRussia
  4. 4.National Research University Higher School of EconomicsMoscowRussia
  5. 5.Department of MathematicsRice UniversityHoustonUSA
  6. 6.Department of MathematicsUniversity of WashingtonSeattleUSA

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