Lipschitz equivalence of self-similar sets with triangular pattern |
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| Authors: | ZHU ZhiYong XIONG Ying & XI LiFeng School of Mathematics Statistics Huazhong University of Science Technology Wuhan China |
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| Affiliation: | ZHU ZhiYong1,XIONG Ying2 & XI LiFeng3,1School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China,2Department of Mathematics,South China University of Technology,Guangzhou 510641,3Institute of Mathematics,Zhejiang Wanli University,Ningbo 315100 |
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| Abstract: | In this paper, we discuss the Lipschitz equivalence of self-similar sets with triangular pattern. This is a generalization of {1, 3, 5}-{1, 4, 5} problem proposed by David and Semmes. It is proved that if two such self-similar sets are totally disconnected, then they are Lipschitz equivalent if and only if they have the same Hausdorff dimension. |
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| Keywords: | fractal Lipschitz equivalence triangular pattern self-similar set |
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