Lipschitz equivalence of self-similar sets and hyperbolic boundaries |
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Authors: | Jun Jason Luo Ka-Sing Lau |
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Institution: | 1. Department of Mathematics, The Chinese University of Hong Kong, Hong Kong;2. Department of Mathematics, Shantou University, Shantou, Guangdong 515063, PR China |
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Abstract: | Kaimanovich (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. |
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Keywords: | Augmented tree Hyperbolic boundary Incidence matrix Lipschitz equivalence OSC Primitive Rearrangeable Self-similar set Self-affine set |
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