| Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets |
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| 引用本文： | Li-feng XI~(1 ) Huo-jun RUAN~2 1 Institute of Mathematics,Zhejiang Wanli University,Ningbo 315100,China, 2 Department of Mathematics,Zhejiang University,Hangzhou 310027,China. Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets[J]. 中国科学A辑(英文版), 2007, 50(11): 1537-1551. DOI: 10.1007/s11425-007-0113-5 |
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| 作者姓名： | Li-feng XI~(1 ) Huo-jun RUAN~2 1 Institute of Mathematics Zhejiang Wanli University Ningbo 315100 China 2 Department of Mathematics Zhejiang University Hangzhou 310027 China |
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| 作者单位： | Li-feng XI（Institute of Mathematics,Zhejiang Wanli University,Ningbo 315100,China） ;Huo-jun RUAN（Department of Mathematics,Zhejiang University,Hangzhou 310027,China） ; |
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| 摘 要： | This paper investigates the Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets D=(r_1D)∪(r_2D (1 r_1-r_2-r_3)/2)∪(r_3D 1 r_3) and E=(r_1E)∪(r_2E 1-r_2- r_3)∪(r_3E 1-r_3),and proves that D and E are Lipschitz equivalent if and only if there are positive integers m and n such that r_1~m=r_3~n.
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| 收稿时间： | 2005-04-16 |
| 修稿时间： | 2006-05-04 |
Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets |
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| Li-feng Xi,Huo-jun Ruan. Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets[J]. Science in China(Mathematics), 2007, 50(11): 1537-1551. DOI: 10.1007/s11425-007-0113-5 |
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| Authors: | Li-feng Xi Huo-jun Ruan |
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| Affiliation: | 1. Institute of Mathematics,Zhejiang Wanli University,Ningbo 315100,China
2. Department of Mathematics,Zhejiang University,Hangzhou 310027,China |
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| Abstract: | This paper investigates the Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets D = (r 1 D) ∪ (r 2 D + (1 + r 1−r 2−r 3)/2) ∪ (r 3 D + 1−r 3) and E = (r 1 E) ∪ (r 2 E + 1−r 2−r 3) ∪ (r 3 E + 1−r 3), and proves that D and E are Lipschitz equivalent if and only if there are positive integers m and n such that r 1 m = r 3 n . This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10301029, 10671180, 10601049) and Morningside Center of Mathematics |
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| Keywords: | self-similar set overlap Lipschitz equivalence graph-directed construction ergodicity martingale |
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