CONTINUITY OF SUBADDITIVE PRESSURE FOR SELF-AFFINE SETS

被引：1

作者：

Falconer, Kenneth ^{[1
]}

Sloan, Arron ^{[1
]}

机构：

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

来源：

REAL ANALYSIS EXCHANGE | 2008年 / 34卷 / 02期

关键词：

pressure; subadditive; submultiplicative; fractal; self-affine;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A 'pressure' functional phi(s) (T-1,...,T-N),defined as the limit of sums of singular value functions of products of linear mappings (T-1,...,T-N),is central in analysing fractal dimensions of self-affine sets. We investigate the continuity of phi(s) with respect to the linear mappings (T-1,...,T-N) which underlie the self-affine sets.

引用

页码：413 / 427

页数：15

共 12 条

[1]

Falconer K.J., 2003, FRACTAL GEOMETRY

[2] Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices [J].

Falconer, Kenneth ;

Miao, Jun .

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2007, 15 (03) :289-299

[3]

FENG DJ, ISRAEL J MA IN PRESS

[4] FALCONERS FORMULA FOR THE HAUSDORFF DIMENSION OF A SELF-AFFINE SET IN R(2) [J].

HUETER, I ;

LALLEY, SP .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1995, 15 :77-97

[5] FRACTALS AND SELF SIMILARITY [J].

HUTCHINSON, JE .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1981, 30 (05) :713-747

[6] Hausdorff dimension for randomly perturbed self affine attractors [J].

Jordan, Thomas ;

Pollicott, Mark ;

Simon, Karoly .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2007, 270 (02) :519-544

[7] Overlapping self-affine sets of Kakeya type [J].

Kaenmaki, Antti ;

Shmerkin, Pablo .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2009, 29 :941-965

[8]

Peres Y, 2000, PROG PROBAB, V46, P95

[9] Measure and dimension for some fractal families [J].

Solomyak, B .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1998, 124 :531-546

[10] Quasi-Bemoulli measure in its week meaning: results and examples [J].

Testud, B .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2006, 42 (01) :1-35

← 1 2 →