齐次均匀Moran集的拟Lipschitz等价

陈咸存, 奚李峰

数学学报 ›› 2010, Vol. 53 ›› Issue (4) : 733-740.

PDF(396 KB)
PDF(396 KB)
数学学报 ›› 2010, Vol. 53 ›› Issue (4) : 733-740. DOI: 10.12386/A2010sxxb0082
论文

齐次均匀Moran集的拟Lipschitz等价

    陈咸存1, 奚李峰2
作者信息 +

Quasi-Lipschitz Equivalence on Homogeneous Uniform Moran Sets

    Xian Cun CHEN1, Li Feng XI2
Author information +
文章历史 +

摘要

本文证明了两个正则齐次均匀Moran集拟Lipschitz等价当且仅当它们的Hausdorff维数相等.

Abstract

This paper proves that two regular homogeneous uniform Moran sets are quasi-Lipschitz equivalent if and only if they have the same Hausdorff dimension.

关键词

分形 / Moran集 / 拟Lipschitz等价

Key words

fractal / Moran set / quasi-Lipschitz equivalence

引用本文

导出引用
陈咸存, 奚李峰. 齐次均匀Moran集的拟Lipschitz等价. 数学学报, 2010, 53(4): 733-740 https://doi.org/10.12386/A2010sxxb0082
Xian Cun CHEN, Li Feng XI. Quasi-Lipschitz Equivalence on Homogeneous Uniform Moran Sets. Acta Mathematica Sinica, Chinese Series, 2010, 53(4): 733-740 https://doi.org/10.12386/A2010sxxb0082

参考文献


[1] Cooper D., Pignataro T., On the shape of Cantor sets, J. Differential Geom., 1988, 28(2): 203--221.

[2] David G., Semmes S., Fractured Fractals and Broken Dreams, Self-similar Geometry Through Metric and Measure, volume 7 of Oxford Lecture Series in Mathematics and its Applications, New York: The Clarendon Press Oxford University Press, 1997.

[3] Falconer K. J., Marsh D. T., Classification of quasi-circles by Hausdorff dimension, Nonlinearity, 1989, 2(3): 489--493.

[4] Falconer K. J., Marsh D. T., On the Lipschitz equivalence of Cantor sets, Mathematika, 1992, 39(2): 223--233.

[5] Falconer K. J., {Techniques in Fractal Geometry}, Chichester: John Wiley & Sons Ltd., 1997.

[6] Feng D. J., Wen Z. Y., Wu J. Some dimensional results for homogeneous Moran sets, Sci. China Ser. A, 1997, 40(5): 475--482.

[7] Guo Q. L., Xi L. F., Whitney sets and graph-directed arcs, Acta Mathematica Sinica, Chinese Series, 2007, 50(1): 25--32.

[8] Mauldin R. D., Williams S. C., Hausdorff dimension in graph directed constructions, Trans. Amer. Math. Soc., 1988, 309(2): 811--829.

[9] Rao H., Ruan H. J., Xi L. F., Lipschitz equivalence of self-similar sets, C. R. Math. Acad. Sci. Paris, 2006, 342(3): 191--196.

[10] Xi L. F., Lipschitz equivalence of self-conformal sets, J. London Math. Soc. (2), 2004, 70(2): 369--382.

[11] Xi L. F., Quasi-{L}ipschitz equivalence of fractals, Israel J. Math., 2007, 160: 1--21.

[12] Xi L. F., Ruan H. J., Lipschitz equivalence of generalized {1,3,5,}-{1,4,5} self-similar sets, Sci. China Ser. A, 2007, 50(11): 1537--1551.

[13] Xi L. F., Ruan H. J., Guo Q. L., Sliding of self-similar sets, Sci. China Ser. A, 2007, 50(3): 351--360.

[14] Xi L. F., Ruan H. J., Lipschitz equivalence of self-similar sets satisfying the strong separation condition, Acta Mathematica Sinica, Chinese Series, 2008, 51(3): 493--500.

基金

国家自然科学基金资助项目(10671180)

PDF(396 KB)

218

Accesses

0

Citation

Detail

段落导航
相关文章

/