
齐次均匀Moran集的拟Lipschitz等价
Quasi-Lipschitz Equivalence on Homogeneous Uniform Moran Sets
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.
This paper proves that two regular homogeneous uniform Moran sets are quasi-Lipschitz equivalent if and only if they have the same Hausdorff dimension.
分形 / Moran集 / 拟Lipschitz等价 {{custom_keyword}} /
fractal / Moran set / quasi-Lipschitz equivalence {{custom_keyword}} /
[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.
国家自然科学基金资助项目(10671180)
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