BILIPSCHITZ EMBEDDING OF SELF-SIMILAR SETS

被引：24

作者：

Deng, Juan ^{[2
]}

Wen, Zhi-Ying ^{[2
]}

Xiong, Ying ^{[3
]}

Xi, Li-Feng ^{[1
]}

机构：

[1] Zhejiang Wanli Univ, Inst Math, Ningbo 315100, Zhejiang, Peoples R China

[2] Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China

[3] S China Univ Technol, Dept Math, Guangzhou 510641, Guangdong, Peoples R China

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2011年 / 114卷

关键词：

LIPSCHITZ EQUIVALENCE; HAUSDORFF DIMENSION; CONFORMAL SETS; CANTOR SETS; FRACTALS;

D O I：

10.1007/s11854-011-0012-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove that each self-similar set satisfying the strong separation condition can be bilipschitz embedded into each self-similar set with larger Hausdorff dimension. A bilipschitz embedding between two self-similar sets of the same Hausdorff dimension both satisfying the strong separation condition is only possible if the two sets are bilipschitz equivalent.

引用

页码：63 / 97

页数：35

共 26 条

[1] [Anonymous], 1995, Geometry of Sets and Measures in Euclidean Spaces
[2] Bonk M., 2006, INT C MATH EUR MATH, VII, P1349
[3] COOPER D, 1988, J DIFFER GEOM, V28, P203
[4] David G., 1997, OXFORD LECT SERIES M, V7
[5] Falconer K., 1997, Techniques in Fractal Geometry
[6] Classification of quasi-circles by Hausdorff dimension
Falconer, K. J.
Marsh, D. T.
[J]. NONLINEARITY, 1989, 2 (03) : 489 - 493
[7] DIMENSIONS AND MEASURES OF QUASI SELF-SIMILAR SETS
FALCONER, KJ
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 106 (02) : 543 - 554
[8] ON THE LIPSCHITZ EQUIVALENCE OF CANTOR SETS
FALCONER, KJ
MARSH, DT
[J]. MATHEMATIKA, 1992, 39 (78) : 223 - 233
[9] A rigidity theorem for the solvable Baumslag-Solitar groups
Farb, B
Mosher, L
[J]. INVENTIONES MATHEMATICAE, 1998, 131 (02) : 419 - 451
[10] FRACTALS AND SELF SIMILARITY
HUTCHINSON, JE
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1981, 30 (05) : 713 - 747

← 1 2 3 →