English

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

R2 v1 2026-06-23T02:40:24.937Z