Lipschitz equivalence of fractal sets in ℝ

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

“…Rao, Ruan and Xi [22] gave an affirmative answer to this question by introducing the graph‐directed technique to prove certain self‐similar sets being Lipschitz equivalence. Although considerable efforts [5, 10, 15–18, 20–25, 27–38] have been made in the study of this issue, it is still a long way to understand the Lipschitz equivalence of self‐similar sets.…”

Self‐similar sets, simple augmented trees and their Lipschitz equivalence

“…The Lipschitz equivalence of Cantor sets was first considered in . For its extension on self‐similar sets, it has been undergoing rapid development recently . However, most of the studies are based on the nice geometric structure of self‐similar sets such as Cantor sets or totally disconnected self‐similar sets with the open set condition ( OSC ).…”

Lipschitz equivalence of self-similar sets and hyperbolic boundaries II

“…The recent interest was due to Rao, Ruan and Xi [15] on their path breaking solution to a question of David and Semmes, so called the {1, 3, 5} − {1, 4, 5} problem. For the developments and the generalizations, the reader can refer to [2,16,17,21,22,23,24,25] for more details. In particular, in [24], the Lipschitz classification of self-similar sets with exponentially commensurable contraction ratios is characterized in terms of the ideal classes in algebra.…”