Journal of East China Normal University(Natural Science) >

2015 , Vol. 2015 >Issue 1: 68 - 74

DOI: https://doi.org/10.3969/j.issn.1000-5641.2015.01.008

Article

Lipschitz equivalence of dust-like Lalley self-affine sets

  • LI Wen-Wen ,
  • MA Yu-Tian
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  • 1. Department of Mathematics, East China Normal University, Shanghai 200241, China;
    2. Department of Mathematics, Fuyang Teachers College, Fuyang Anhui 236037, China

Received date: 2014-02-01

  Online published: 2015-03-29

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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.

Key words： dust-like; Lalley sets; Lipschitz equivalenc

Cite this article

LI Wen-Wen , MA Yu-Tian . Lipschitz equivalence of dust-like Lalley self-affine sets[J]. Journal of East China Normal University(Natural Science), 2015 , 2015(1) : 68 -74 . DOI: 10.3969/j.issn.1000-5641.2015.01.008

References

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.
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