The sets of divergence points of self-similar measures are residual

被引：19

作者：

Li, Jinjun ^{[1
]}

Wu, Min ^{[2
]}

机构：

[1] Zhangzhou Normal Univ, Dept Math, Zhangzhou 363000, Peoples R China

[2] S China Univ Technol, Dept Math, Guangzhou 510641, Guangdong, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 404卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Self-similar measure; Open set condition; Divergence point; Residual; SPECIFICATION PROPERTY; TOPOLOGICAL PRESSURE; NONNORMAL POINTS; BAIRE CATEGORY; DIMENSION; AVERAGES; ENTROPY; NUMBERS;

D O I：

10.1016/j.jmaa.2013.03.043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let mu be a self-similar measure supported on a self-similar set K with the open set condition. For x is an element of K, let A(D(x)) be the set of accumulation points of D-r(x) = log mu(B(x.r))/logr as r SE arrow 0. In this paper, we show that for any closed non-singleton subinterval I subset of R, the set of points x for which the set A(D(x)) equals I is either empty or residual. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：429 / 437

页数：9

共 23 条

[1] Topological and fractal properties of real numbers which are not normal [J].

Albeverio, S ;

Pratsiovytyi, M ;

Torbin, G .

BULLETIN DES SCIENCES MATHEMATIQUES, 2005, 129 (08) :615-630

[2] BAIRE CATEGORY AND EXTREMELY NON-NORMAL POINTS OF INVARIANT SETS OF IFS'S [J].

Baek, In-Soo ;

Olsen, Lars .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 27 (03) :935-943

[3] Sets of "non-typical" points have full topological entropy and full Hausdorff dimension [J].

Barreira, L ;

Schmeling, J .

ISRAEL JOURNAL OF MATHEMATICS, 2000, 116 (1) :29-70

[4]

Barreira L., PREPRINT

[5] The pointwise dimension of self-similar measures [J].

Chen, EC ;

Xiong, JC .

CHINESE SCIENCE BULLETIN, 1999, 44 (23) :2136-2140

[6]

Falconer K., 1997, Techniques in Fractal Geometry

[7] Recurrence, dimension and entropy [J].

Fan, AH ;

Feng, DJ ;

Wu, J .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2001, 64 :229-244

[8] Multifractal formalism for self-similar measures with weak separation condition [J].

Feng, De-Jun ;

Lau, Ka-Sing .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2009, 92 (04) :407-428

[9] Ergodic limits on the conformal repellers [J].

Feng, DJ ;

Lau, KS ;

Wu, J .

ADVANCES IN MATHEMATICS, 2002, 169 (01) :58-91

[10] ON BANDTS TANGENTIAL DISTRIBUTION FOR SELF-SIMILAR MEASURES [J].

GRAF, S .

MONATSHEFTE FUR MATHEMATIK, 1995, 120 (3-4) :223-246

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