On the packing measure of the Sierpinski gasket

被引：4

作者：

Llorente, Marta ^{[1
]}

Eugenia Mera, M. ^{[2
]}

Moran, Manuel ^{[2
,3
]}

机构：

[1] Univ Autonoma Madrid, Dept Anal Econ Econ Cuantitat, Campus Cantoblanco, E-28049 Madrid, Spain

[2] Univ Complutense Madrid, Dept Anal Econ & Econ Cuantitat, Campus Somosaguas, Madrid 28223, Spain

[3] Univ Complutense Madrid, IMI Inst Interdisciplinary Math, E-28040 Madrid, Spain

来源：

NONLINEARITY | 2018年 / 31卷 / 06期

关键词：

Sierpinski gasket; packing measure; computability of fractal measures; algorithm; self-similar sets; CENTERED HAUSDORFF MEASURES; SELF-SIMILAR SETS; COMPUTABILITY; EQUATIONS;

D O I：

10.1088/1361-6544/aab31c

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the s-dimensional packing measure P-s(S) of the Sierpinski gasket S, where s = log 3/log 2 is the similarity dimension of S, satisfies 1.6677 <= P-s(S) <= 1.6713. The formula presented in theorem 6 enables the achievement of the above measure bounds for this non-totally disconnected set as it shows that the symmetries of the Sierpinski gasket can be exploited to simplify the density characterization of P-s obtained in Moran (2005 Nonlinearity 18 559-70) for self-similar sets satisfying the so-called open set condition. Thanks to the reduction obtained in theorem 6 we are able to handle the problem of computability of P-s(S) with a suitable algorithm.

引用

页码：2571 / 2589

页数：19

共 45 条

[1] SOME PROPERTIES OF THE SPECTRUM OF THE SIERPINSKI GASKET IN A MAGNETIC-FIELD [J].