Birkhoff sum fluctuations in substitution dynamical systems
SCIE
SCOPUS
- Title
- Birkhoff sum fluctuations in substitution dynamical systems
- Authors
- Elliot Paquette; SON, YOUNGHWAN
- Date Issued
- 2019-07
- Publisher
- CAMBRIDGE UNIV PRESS
- Abstract
- We consider the deviation of Birkhoff sums along fixed orbits of substitution dynamical systems. We show distributional convergence for the Birkhoff sums of eigen functions of the substitution matrix. For non-coboundary eigen functions with eigen value of modulus 1, we obtain a central limit theorem. For other eigen functions, we show convergence to distributions supported on Cantor sets. We also give a new criterion for such an eigen function to be a coboundary, as well as a new characterization of substitution dynamical systems with bounded discrepancy.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/94693
- DOI
- 10.1017/etds.2017.83
- ISSN
- 0143-3857
- Article Type
- Article
- Citation
- ERGODIC THEORY AND DYNAMICAL SYSTEMS, vol. 39, page. 1971 - 2005, 2019-07
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