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arXiv 2608.16471math.MGmath.CA

自相似集之间的Lipschitz满射

Lipschitz surjections between self-similar sets

Attila Gáspár

AI总结:

本文针对相似比可公度的同维度尘状自相似集,刻画了其之间Lipschitz满射的存在性,且该结果可推广至图导向分形。

AI中文摘要:

在相似比可公度的假设下,我们给出了相同维度尘状自相似集之间Lipschitz满射存在性的刻画,该结果更一般地适用于图导向分形。

英文摘要:

We give a characterization of the existence of Lipschitz surjections between dust-like self-similar sets of the same dimension under the assumption that the similarity ratios are commensurable. Our results apply more generally to graph-directed fractals.

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