A note on the run length function for intermittent maps

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:472

Article

Cui, Hongfei¹  Fang, Lulu²  Zhang, Yiwei³ 

[1] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Hubei, Peoples R China

[2] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Guangdong, Peoples R China

[3] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Ctr Math Sci, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China

关键词: Run length function;    Intermittent maps;    Erdos-Renyi law;   

DOI  :  10.1016/j.jmaa.2018.11.058

来源: Elsevier

【 摘 要 】

We study the run length function for intermittent 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 intermittent maps. Our results are compensational to the Erdos-Renyi law obtained by Denker and Nicol in [8]. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free