Limiting curves for polynomial adic systems
Dynamical Systems
2017-01-27 v1
Abstract
We prove the existence and describe limiting curves resulting from deviations in partial sums in the ergodic theorem for cylindrical functions and polynomial (self-similar) adic systems. For a general ergodic measure-preserving transformation and a summable function we give a necessary condition for a limiting curve to exist. Our work generalizes results by \'E. Janvresse, T. de la Rue and Y. Velenik and answers several questions from their work.
Keywords
Cite
@article{arxiv.1701.07617,
title = {Limiting curves for polynomial adic systems},
author = {Aleksei Minabutdinov},
journal= {arXiv preprint arXiv:1701.07617},
year = {2017}
}
Comments
26 pages,11 figures