METRIC THEOREM AND HAUSDORFF DIMENSION ON RECURRENCE RATE OF LAURENT SERIES

被引：3

作者：

Hu, Xue-hai ^{[1
]}

Li, Bing ^{[2
]}

Xu, Jian ^{[3
]}

机构：

[1] Huazhong Agr Univ, Coll Sci, Wuhan 430070, Hubei, Peoples R China

[2] S China Univ Technol, Dept Math, Guangzhou 510640, Guangdong, Peoples R China

[3] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2014年 / 51卷 / 01期

关键词：

recurrence rate; pointwise dimension; continued fractions; Laurent series; Hausdorff dimension; POINCARE RECURRENCE; CONTINUED FRACTIONS; SETS; SPECTRUM;

D O I：

10.4134/BKMS.2014.51.1.157

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the recurrence rates of Laurent series about continued fractions almost surely coincide with their pointwise dimensions of the Haar measure. Moreover, let E-alpha,E-beta be the set of points with lower and upper recurrence rates alpha, beta (0 <= alpha <= beta <= infinity), we prove that all the sets E-alpha,E-beta are of full Hausdorff dimension. Then the recurrence sets E-alpha,E-beta have constant multifractal spectra.

引用

页码：157 / 171

页数：15

共 16 条

[1] Quadratic bodies in areas of higher conguence. I. (Arithmetic part) [J].

Artin, E .

MATHEMATISCHE ZEITSCHRIFT, 1924, 19 :153-206

[2] Product structure of Poincare recurrence [J].

Barreira, L ;

Saussol, B .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2002, 22 :33-61

[3] Hausdorff dimension of measures via Poincare recurrence [J].

Barreira, L ;

Saussol, B .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 219 (02) :443-463

[4]

Berthe V., 2000, Expo. Math., V18, P257

[5] QUANTITATIVE RECURRENCE RESULTS [J].

BOSHERNITZAN, MD .

INVENTIONES MATHEMATICAE, 1993, 113 (03) :617-631

[6]

Falconer KJ, 1999, Fractal geometry: mathematical foundations and applications

[7] The Hausdorff dimension of recurrent sets in symbolic spaces [J].

Feng, DJ ;

Wu, J .

NONLINEARITY, 2001, 14 (01) :81-85

[8] Cantor sets determined by partial quotients of continued fractions of Laurent series [J].

Hu, Xue-Hai ;

Wang, Bao-Wei ;

Wu, Jun ;

Yu, Yue-Li .

FINITE FIELDS AND THEIR APPLICATIONS, 2008, 14 (02) :417-437

[9] The spectrum of Poincare recurrence [J].

Lau, Ka-Sing ;

Shu, Lin .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2008, 28 :1917-1943

[10] Linear complexity profiles: Hausdorff dimensions for almost perfect profiles and measures for general profiles [J].

Niederreiter, H ;

Vielhaber, M .

JOURNAL OF COMPLEXITY, 1997, 13 (03) :353-383

← 1 2 →