Hausdorff dimension 2 for Julia sets of quadratic polynomials

被引：0

作者：

Stefan-M. Heinemann

Bernd O. Stratmann

机构：

[1] TU Clausthal,

[2] Institut für Theoretische Physik,undefined

[3] D-38678 Clausthal-Zellerfeld,undefined

[4] Germany (e-mail: Stefan.Heinemann@TU-Clausthal.DE) ,undefined

[5] University of St Andrews,undefined

[6] Mathematical Institute,undefined

[7] St Andrews,undefined

[8] KY16 9SS,undefined

[9] Scotland (e-mail: bos@st-and.ac.uk) ,undefined

来源：

Mathematische Zeitschrift | 2001年 / 237卷

关键词：

Hausdorff Dimension; Quadratic Polynomial;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We consider families of quadratic polynomials which admit parameterisations in a neighbourhood of the boundary of the Mandelbrot set. We show how to find parameters such that the associated Julia sets are of Hausdorff dimension 2.

引用

下载

页码：571 / 583

页数：12

共 50 条

[21] On the Hausdorff dimension of Julia sets of meromorphic functions .2.
Kotus, J
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1995, 123 (01): : 33 - 46
[22] Hausdorff Dimension of Julia Sets in the Logistic Family
Neil Dobbs
Jacek Graczyk
Nicolae Mihalache
Communications in Mathematical Physics, 2023, 399 : 673 - 716
[23] HAUSDORFF DIMENSION OF JULIA SETS OF UNICRITICAL CORRESPONDENCES
Siqueira, Carlos
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, 151 (02) : 633 - 645
[24] HAUSDORFF DIMENSION AND BIACCESSIBILITY FOR POLYNOMIAL JULIA SETS
Meerkamp, Philipp
Schleicher, Dierk
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 141 (02) : 533 - 542
[25] THE HAUSDORFF DIMENSION OF JULIA SETS OF MEROMORPHIC FUNCTIONS
STALLARD, GM
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1994, 49 : 281 - 295
[26] Julia sets, Hausdorff dimension and phase transition
Gao, Junyang
CHAOS SOLITONS & FRACTALS, 2011, 44 (10) : 871 - 877
[27] ESCAPE RATES AND HAUSDORFF DIMENSION OF JULIA SETS
ECKHARDT, B
CHAOS SOLITONS & FRACTALS, 1993, 3 (04) : 387 - 394
[28] Hausdorff dimension and Hausdorff measures of Julia sets of elliptic functions
Kotus, J
Urbanski, M
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2003, 35 : 269 - 275
[29] Calculating Hausdorff dimension of Julia sets and Kleinian limit sets
Jenkinson, O
Pollicott, M
AMERICAN JOURNAL OF MATHEMATICS, 2002, 124 (03) : 495 - 545
[30] On the continuity of Hausdorff dimension of Julia sets and similarity between the Mandelbrot set and Julia sets
Rivera-Letelier, J
FUNDAMENTA MATHEMATICAE, 2001, 170 (03) : 287 - 317

← 1 2 3 4 5 →