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- W4380320037 abstract "Let E=K(n,m,D) be a Bedford-McMullen carpet with expanding factors n,m and digit set D. We call a=(aj)j=0m−1 the distribution sequence of D whereaj=#{i;(i,j)∈D}. Under a certain vertical separation condition, Li et al. [Lipschitz equivalence of McMullen sets, Fractals, 21(3 & 4)(2013), 1350022, 11 pages] showed that if two totally disconnected Bedford-McMullent carpets share the same distribution sequence, then they are Lipschitz equivalent. In this paper, we define a metric ρ on D∞ and call (D∞,ρ) a half-symbolic space. We show that if E is totally disconnected and satisfies the vertical separation condition, then E is Lipschitz equivalent to (D∞,ρ). Thanks to this result, we extends the result of Li et al. by showing that two Bedford-McMullen carpets K(n,m,D) and K(n,m,D′) are Lipschitz equivalent if a, the distribution sequence of D, is a permutation of a′, the distribution sequence of D′, and that a and a′ satisfy a certain color matchable condition." @default.
- W4380320037 created "2023-06-13" @default.
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- W4380320037 date "2023-12-01" @default.
- W4380320037 modified "2023-09-25" @default.
- W4380320037 title "Constructing bi-Lipschitz maps between Bedford-McMullen carpets via symbolic spaces" @default.
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- W4380320037 doi "https://doi.org/10.1016/j.jmaa.2023.127514" @default.
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