Projections of Self-Similar and Related Fractals: A Survey of Recent Developments

被引：29

作者：

Shmerkin, Pablo ^{[1
,2
]}

机构：

[1] Torcuato Di Tella Univ, Dept Math & Stat, Buenos Aires, DF, Argentina

[2] Consejo Nacl Invest Cient & Tecn, RA-1033 Buenos Aires, DF, Argentina

来源：

Fractal Geometry and Stochastics V | 2015年 / 70卷

关键词：

Self-similar sets; Self-similar measures; Projections; Hausdorff dimension; L-q dimensions; SIMILAR SETS; BERNOULLI CONVOLUTIONS; DIMENSION; ENTROPY; SYSTEMS; FAMILY;

D O I：

10.1007/978-3-319-18660-3_4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In recent years there has been much interest - and progress-in understanding projections of many concrete fractals sets and measures. The general goal is to be able to go beyond general results such as Marstrand's Theorem, and quantify the size of every projection - or at least every projection outside some very small set. This article surveys some of these results and the techniques that were developed to obtain them, focusing on linear projections of planar self-similar sets and measures.

引用

页码：53 / 74

页数：22

共 35 条

[1]

Almarza J., 2014, PREPRINT

[2]

[Anonymous], 2014, FRACTAL GEOMETRY MAT

[3]

DEMOREIRA CGT, 1998, PERIOD MATH HUNG, V37, P55

[4] On a family of symmetric Bernoulli convolutions [J].

Erdos, P .

AMERICAN JOURNAL OF MATHEMATICS, 1939, 61 :974-976

[5] On the smoothness properties of a family of Bernoulli convolutions [J].

Erdos, P .

AMERICAN JOURNAL OF MATHEMATICS, 1940, 62 :180-186

[6]

Eroglu KI, 2007, ANN ACAD SCI FENN-M, V32, P409

[7]

Falconer K.J., 2014, PREPRINT

[8]

Falconer K.J., 2014, INT MATH RE IN PRESS

[9] Exact dimensionality and projections of random self-similar measures and sets [J].

Falconer, Kenneth J. ;

Jin, Xiong .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2014, 90 :388-412

[10] Relationships between different dimensions of a measure [J].

Fan, AH ;

Lau, KS ;

Rao, H .

MONATSHEFTE FUR MATHEMATIK, 2002, 135 (03) :191-201

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