Lipschitz equivalence of self-similar sets and hyperbolic boundaries
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AbstractKaimanovich (2003) [9] introduced the concept of augmented tree on the symbolic space of a self-similar set. It is hyperbolic in the sense of Gromov, and it was shown by Lau and Wang (2009) [12] that under the open set condition, a self-similar set can be identified with the hyperbolic boundary of the tree. In the paper, we investigate in detail a class of simple augmented trees and the Lipschitz equivalence of such trees. The main purpose is to use this to study the Lipschitz equivalence problem of the totally disconnected self-similar sets which has been undergoing some extensive development recently. (C) 2012 Elsevier Inc. All rights reserved.
All Author(s) ListLuo JJ, Lau KS
Journal nameAdvances in Mathematics
Year2013
Month3
Day1
Volume Number235
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Pages555 - 579
ISSN0001-8708
eISSN1090-2082
LanguagesEnglish-United Kingdom
KeywordsAugmented tree; Hyperbolic boundary; Incidence matrix; Lipschitz equivalence; OSC; Primitive; Rearrangeable; Self-affine set; Self-similar set
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2021-16-01 at 00:41