Hausdorff dimension of Julia sets of Feigenbaum polynomials with high criticality

被引：6

作者：

Levin, G ^{[1
]}

Swiatek, G

机构：

[1] Hebrew Univ Jerusalem, Dept Math, IL-91904 Jerusalem, Israel

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2005年 / 258卷 / 01期

关键词：

D O I：

10.1007/s00220-005-1332-7

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider unimodal polynomials with Feigenbaum topological type and critical points whose orders tend to infinity. It is shown that the hyperbolic dimensions of their Julia set go to 2; furthermore, that the Hausdorff dimensions of the basins of attraction of their Feigenbaum attractors also tend to 2. The proof is based on constructing a limiting dynamics with a flat critical point.

引用

页码：135 / 148

页数：14

共 11 条

[1] Wild Cantor attractors exist [J].

Bruin, H ;

Keller, G ;

Nowicki, T ;

vanStrien, S .

ANNALS OF MATHEMATICS, 1996, 143 (01) :97-130

[2]

Eckmann J.-P., 1985, LECT NOTES PHYS, V227

[3] ANALYTICITY PROPERTIES OF THE FEIGENBAUM FUNCTION [J].

EPSTEIN, H ;

LASCOUX, J .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1981, 81 (03) :437-453

[4] Collet, Eckmann and Holder [J].

Graczyk, J ;

Smirnov, S .

INVENTIONES MATHEMATICAE, 1998, 133 (01) :69-96

[5]

LEVI G, IN PRESS ISRAEL MATH

[6] Thickness of Julia sets of Feigenbaum polynomials with high order critical points [J].

Levin, G ;

Swiatek, G .

COMPTES RENDUS MATHEMATIQUE, 2004, 339 (06) :421-424

[7]

LEVIN G, IN PRESS COMMUN MATH

[8]

Mc Mullen C, 1998, ANN MATH STUDIES, V142

[9] AREA AND HAUSDORFF DIMENSION OF JULIA SETS OF ENTIRE-FUNCTIONS [J].

MCMULLEN, C .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 300 (01) :329-342

[10]

Przytycki F, 1998, FUND MATH, V155, P189

← 1 2 →