Abstract
In this paper, we prove that each self-similar set satisfying the strong separation condition can be bilipschitz embedded into each self-similar set with larger Hausdorff dimension. A bilipschitz embedding between two self-similar sets of the same Hausdorff dimension both satisfying the strong separation condition is only possible if the two sets are bilipschitz equivalent.
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This work was supported by NSFC (Grants 11071224, 11071082, 10631040, 61071066) and the Morningside Center of Mathematics.
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Deng, J., Wen, Zy., Xiong, Y. et al. Bilipschitz embedding of self-similar sets. JAMA 114, 63–97 (2011). https://doi.org/10.1007/s11854-011-0012-0
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DOI: https://doi.org/10.1007/s11854-011-0012-0