2012
DOI: 10.1090/s0002-9947-2011-05327-4
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Lipschitz equivalence of Cantor sets and algebraic properties of contraction ratios

Abstract: Abstract. In this paper we investigate the Lipschitz equivalence of dust-like self-similar sets in R d . One of the fundamental results by Falconer and Marsh [On the Lipschitz equivalence of Cantor sets, Mathematika, 39 (1992), 223-233] establishes conditions for Lipschitz equivalence based on the algebraic properties of the contraction ratios of the self-similar sets. In this paper we extend the study by examining deeper such connections.A key ingredient of our study is the introduction of a new equivalent re… Show more

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Cited by 57 publications
(49 citation statements)
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“…Lipschitz equivalence of fractals is also an interesting topic [2,11,5,33,32,25,35,[43][44][45][46][47][48][49]. Let's consider the Lipschitz equivalence of the self-similar set…”
Section: Resultsmentioning
confidence: 99%
“…Lipschitz equivalence of fractals is also an interesting topic [2,11,5,33,32,25,35,[43][44][45][46][47][48][49]. Let's consider the Lipschitz equivalence of the self-similar set…”
Section: Resultsmentioning
confidence: 99%
“…The Lipschitz embedding of fractals can be found in Llorente and Mattila [15], Mattila and Saaranen [16] and Deng and Wen et al [5]. Please also refer to Rao, Ruan and Yang [21] and Rao, Ruan and Wang [22].…”
Section: +mentioning
confidence: 99%
“…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 ).…”
Section: Introductionmentioning
confidence: 99%