Orbits closeness for slowly mixing dynamical systems

被引：0

作者：

Rousseau, Jerome ^{[1
,2
,3
]}

Todd, Mike ^{[4
]}

机构：

[1] Acad Mil St Cyr Coetquidan, Acad Mil St Cyr Coetquidan, F-56381 Guer, France

[2] Univ Rennes 1, IRMAR, CNRS UMR 6625, F-35042 Rennes, France

[3] Univ Fed Bahia, Dept Matemat, Ave Ademar Barros S-N, BR-40170110 Salvador, BA, Brazil

[4] Univ St Andrews, Math Inst, St Andrews KY16 9SS, Scotland

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2024年 / 44卷 / 04期

关键词：

shortest distance; longest common substring; correlation dimension; inducing schemes; MULTIFRACTAL ANALYSIS; CORRELATION DIMENSION; RECURRENCE; SPECTRUM;

D O I：

10.1017/etds.2023.50

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a dynamical system, we prove that the shortest distance between two n-orbits scales like n to a power even when the system has slow mixing properties, thus building and improving on results of Barros, Liao and the first author [On the shortest distance between orbits and the longest common substring problem. Adv. Math. 344 (2019), 311-339]. We also extend these results to flows. Finally, we give an example for which the shortest distance between two orbits has no scaling limit.

引用

页码：1192 / 1208

页数：17

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