Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta $$\end{document}-Weakly Mixing Subsets Along a Collection of Sequences of Integers

被引：0
作者：
Jian Li
Kairan Liu
机构：
[1] Shantou University,Department of Mathematics
[2] University of Science and Technology of China,Department of Mathematics
来源：
Journal of Dynamics and Differential Equations | 2021年 / 33卷 / 4期
关键词：
Positive topological entropy; Pinsker ; -algebra; -weakly mixing subset; Characteristic ; -algebra; Good sequences for ; -; -recurrence; 37A35; 37B05; 37B40;
D O I：
10.1007/s10884-020-09898-5
中图分类号：
学科分类号：
摘要：
In this paper, we propose a mild condition, named Condition (∗∗)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(**)$$\end{document}, for collections of sequence of integers and show that for any measure preserving system the Pinsker σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-algebra is a characteristic σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-algebra for the averages along a collection satisfying Condition (∗∗)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(**)$$\end{document}. We introduce the notion of Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta $$\end{document}-weakly mixing subsets along a collection of sequences of integers and show that positive topological entropy implies the existence of Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta $$\end{document}-weakly mixing subsets along a collection of “good” sequences. As a consequence, we show that positive topological entropy implies multi-variant Li–Yorke chaos along polynomial times of the shift prime numbers.
引用
收藏
页码：2155 / 2172
页数：17
相关论文
共 57 条
  • [1] Assani I(1998)Multiple recurrence and almost sure convergence for weakly mixing dynamical systems Isr. J. Math. 103 111-124
  • [2] Bergelson V(1996)Polynomial extensions of van der Waerden’s and Szemerédi’s theorems J. Am. Math. Soc. 9 725-753
  • [3] Leibman A(2002)On Li–Yorke pairs J. Reine Angew. Math. 547 51-68
  • [4] Blanchard F(2008)Entropy sets, weakly mixing sets and entropy capacity Discrete Contin. Dyn. Syst. 20 275-311
  • [5] Glasner E(1996)A pointwise polynomial ergodic theorem for exact endomorphisms and Ann. Inst. H. Poincaré Probab. Statist. 32 765-778
  • [6] Kolyada S(2001)-systems Monatsh. Math. 134 121-141
  • [7] Maass A(2006)Entropy theory from orbit point of view Nonlinearity 19 53-74
  • [8] Blanchard F(2014)Entropy sequences and maximal entropy sets Proc. Am. Math. Soc. 142 137-149
  • [9] Huang W(2016)Positive topological entropy implies chaos DC2 Bull. Hell. Math. Soc. 60 41-90
  • [10] Derrien JM(2013)Some open problems on multiple ergodic averages Isr. J. Math. 194 331-348
123456