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 |
|---|---|
| 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 |
Bibliographical note
Funding Information:A. B. is an Alfred P. Sloan Fellow, a Dynasty Foundation Fellow, and an IUM-Simons Fellow. He is supported in part by the Grant MK 6734.2012.1 of the President of the Russian Federation, by the Programme on Dynamical Systems and Mathematical Control Theory of the Presidium of the Russian Academy of Sciences, by RFBR-CNRS grant 10-01-93115 and by the RFBR grant 11-01-00654.
Funding Information:
B. S. is supported in part by NSF grant DMS-0968879.
Funding
A. B. is an Alfred P. Sloan Fellow, a Dynasty Foundation Fellow, and an IUM-Simons Fellow. He is supported in part by the Grant MK 6734.2012.1 of the President of the Russian Federation, by the Programme on Dynamical Systems and Mathematical Control Theory of the Presidium of the Russian Academy of Sciences, by RFBR-CNRS grant 10-01-93115 and by the RFBR grant 11-01-00654. B. S. is supported in part by NSF grant DMS-0968879.
| Funders | Funder number |
|---|---|
| RFBR-CNRS | 10-01-93115 |
| National Science Foundation | DMS-0968879 |
| Directorate for Mathematical and Physical Sciences | 0968879 |
| Russian Foundation for Basic Research | 11-01-00654 |
| Russian Academy of Sciences |