莫朗集的拟Lipschitz等价

汪沁

数学学报 ›› 2013, Vol. 56 ›› Issue (2) : 187-196.

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数学学报 ›› 2013, Vol. 56 ›› Issue (2) : 187-196. DOI: 10.12386/A2013sxxb0019
论文

莫朗集的拟Lipschitz等价

    汪沁
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Quasi-Lipschitz Equivalence of Moran Fractals

    Qin WANG
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摘要

讨论满足c*>0及s*=s*∈(0,1)条件的莫朗集, 并得到如下结论:任意两个该类型莫朗集彼此拟Lipschitz等价当且仅当它们的Hausdorff维数相等.

Abstract

We consider the class of Moran sets satisfying the conditions c*>0 and s*=s*∈(0, 1). We obtain that two Moran fractals in the class are quasi-Lipschitz equivalent if and only if they have the same Hausdorff dimension.

关键词

分形 / 莫朗集 / 拟Lipschitz等价

Key words

fractal / Moran set / quasi-Lipschitz equivalence

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汪沁. 莫朗集的拟Lipschitz等价. 数学学报, 2013, 56(2): 187-196 https://doi.org/10.12386/A2013sxxb0019
Qin WANG. Quasi-Lipschitz Equivalence of Moran Fractals. Acta Mathematica Sinica, Chinese Series, 2013, 56(2): 187-196 https://doi.org/10.12386/A2013sxxb0019

参考文献

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

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

[3] David G., Semmes S., Fractured Fractals and Broken Dreams: Self-Similar Geometry Through Metric and Measure, Oxford University Press, Oxford, 1997.

[4] Falconer K. J., Techniques in Fractal Geometry, John Wiley & Sons, Ltd., Chichester, 1997.

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

[6] Xi L. F., Xiong Y., Self-similar sets with initial cubic patterns, C. R. Math. Acad. Sci. Paris, 2010, 348(1-2): 15-20.

[7] Xi L. F., Xiong Y., Lipschitz equivalence of fractals generated by nested cubes, Math. Z., 2012, 271: 1287- 1308.

[8] Xi L. F., Quasi-Lipschitz equivalence of fractals, Israel J. Math., 2007, 160: 1-21.

[9] Li H., Wang Q., Xi L. F., Classification of Moran fractals, J. Math. Anal. Appl., 2011, 378(1): 230-237.

[10] Wang Q., Xi L. F., Quasi-Lipschitz equivalence of Ahlfors-David regular sets, Nonlinearity, 2011, 24(3): 941-950.

[11] Wang Q., Xi L. F., Quasi-Lipschitz equivalence of quasi Ahlfors-David regular sets, Sci. China Math., 2011, 54(12): 2573-2582.

[12] Wen Z. Y, Moran sets and Moran classes, Chinese Sci. Bull., 2001, 46(22): 1849-1856.

[13] Mattila P., Saaranen P., Ahlfors-David regular sets and bilipschitz maps, Ann. Acad. Sci. Fenn. Math., 2009, 34: 487-502.

基金

国家自然科学基金(11071224);新世纪优秀人才支持计划;浙江省自然科学基金(LY12F02011)

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