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.
Original language | English |
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Pages (from-to) | 761-789 |
Number of pages | 29 |
Journal | Communications in Mathematical Physics |
Volume | 319 |
Issue number | 3 |
DOIs | |
State | Published - May 2013 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics