A note on the run length function for intermittency maps
Dynamical Systems
2018-11-29 v2
Abstract
We study the run length function for intermittency maps. In particular, we show that the longest consecutive zero digits (resp. one digits) having a time window of polynomial (resp. logarithmic) length. Our proof is relatively elementary in the sense that it only relies on the classical Borel-Cantelli lemma and the polynomial decay of intermittency maps. Our results are compensational to the Erd\H{o}s-R\'{e}nyi law obtained by Denker and Nicol in \cite{dennic13}.
Cite
@article{arxiv.1806.09363,
title = {A note on the run length function for intermittency maps},
author = {Hongfei Cui and Lulu Fang and Yiwei Zhang},
journal= {arXiv preprint arXiv:1806.09363},
year = {2018}
}
Comments
11 pages, Accepted to Journal of Mathematical Analysis and Applications