Algebraic criteria for Lipschitz equivalence of dust-like self-similar sets

作者:Xi, Li-Feng*; Xiong, Ying
来源:Journal of the London Mathematical Society, 2021, 103(2): 760-780.
DOI:10.1112/jlms.12392

摘要

This paper concerns the Lipschitz equivalence of dust-like self-similar sets with commensurable ratios. We obtain an algebraic criterion of Falconer-Marsh type to check whether such two self-similar sets are Lipschitz equivalent, and prove that it is a sufficient and necessary condition.