| Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets |
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| 作者姓名： | Li-feng XI~ |
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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： | 16 April 2005 |
| 修稿时间： | 4 May 2006 |
Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets |
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| Li-feng XI.Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets[J].Science in China(Mathematics),2007,50(11):1537-1551. |
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| Authors: | Li-feng Xi Huo-jun Ruan |
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| Institution: | 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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