自仿射dust-like Lalley集的李卜希兹等价(英)

李雯雯; 马玉田

doi:10.3969/j.issn.1000-5641.2015.01.008

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

自仿射dust-like Lalley集的李卜希兹等价(英)

doi: 10.3969/j.issn.1000-5641.2015.01.008

李雯雯¹,
马玉田^2, ,

1.
华东师范大学数学系上海 200241 2. 阜阳师范学院数学系安徽阜阳 236037

基金项目:

国家自然科学基金(11401104); 安徽省教育厅自然科学一般项目(KJ2012B203); 阜阳师范学院校级重点项目(2014FSKJ032D)

详细信息

作者简介:
李雯雯, 女, 博士, 研究方向为分形几何. E-mail: wenwen200309@163.com.

通讯作者:
马玉田. 男, 博士, 研究方向为分数阶动力系统.

中图分类号: O189
计量
- 文章访问数: 906
- HTML全文浏览量: 6
- PDF下载量: 1007
- 被引次数: 0
出版历程
- 收稿日期: 2014-02-01
- 刊出日期: 2015-01-25

Lipschitz equivalence of dust-like Lalley self-affine sets

LI Wen-Wen¹,
MA Yu-Tian^{2
, ,}

1.
Department of Mathematics, East China Normal University, Shanghai 200241, China;

摘要

摘要: 研究一类自仿射Lalley集,证明了满足dust-like条件的Lalley集E和F是李卜希兹等价的
- 似尘 /
- Lalley集 /
- 李卜希兹等价
Abstract: We consider a class of Lalley self-affine sets and show that two sets E and F from this class are Lipschitz equivalent if they are dust-like.
- dust-like /
- Lalley sets /
- Lipschitz equivalenc

HTML全文

参考文献(1)

[1]

DAVID G, SEMMES S. Fractured Fractals and Broken Dreams: Self-Similar Geometry through Metric and Measure [M]. Oxford Lecture Series in Mathematics and its Applications. Oxford: Oxford Univevsity Press, 1997.
COOPER D, PIGNATARO T. On the shape of cantor sets [J]. J Differ Geom, 1988, 28: 203-221.
WEN Z X, XI L F. Relations among Whitney sets, self-similar arcs and quasi-arcs [J]. Israel J Math, 2003, 136: 251-267.
RAO H, RUAN H J, XI L F. Lipschitz equivalence of self-similar sets [J]. C R Math Acad Sci Paris, 2006, 342: 191-196.
FALCONER K J, MARSH D T. Classification of quasi-circles by Hausdorff dimension [J]. Nonlinearity, 1989, (2): 489-493.
FALCONER K J, MARSH D T. On the Lipschitz equivalence of Cantor sets [J]. Mathematika, 1992, 39: 223-233.
XI L F. Lipschitz equivalence of dust-like self-similar sets [J]. Math Z, 2010, 266: 683-691.
RAO H, RUAN H J, WANG Y. Lipschitz equivalence of Cantor sets and algebraic properties of contraction ratios [M]. Trans Amer Math Soc, 2012, 364: 1109-1126.
XI L F, RUAN H J. Lipschitz equivalence of generalized {1, 3, 5}-{1, 4, 5} self-similar sets [J]. Sci China Ser A, 2007, 50: 1537-1551.
XI L F, RUAN H J, GUO Q L. Sliding of self-similar sets [J]. Sci China Ser A, 2007, 50: 351-360.
WEN Z X, ZHU Z Y, DENG G T. Lipschitz equivalence of a class of general Sierpinski carpets [J]. J Math Anal Appl, 2012, 385: 16-23.
XI L F, XIONG Y. Self-similar sets with initial cubic patterns [J]. C R Math Acad Sci Paris 2010, 348: 15-20.
XI L F, XIONG, Y. Lipschitz equivalence of fractals generated by nested cubes [J]. Math Z, 2012, 271: 1287-1308.
LI B M, LI W X, MIAO J J. Lipschitz equivalence of McMullen sets [J]. Fractals, 2013, 21: id. 1350022.
LALLEY S P, GATZOURAS D, Hausdorff and box dimensions of certain self-affine fractal [J]. Indiana University Mathematics Journal, 1992, 41: 533-568.

施引文献

资源附件(0)

访问统计