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math.GN2012★ 4 cited
Bi-Lipshitz Embedding of Ultrametric Cantor Sets into Euclidean Spaces
Jean V. Bellissard, Antoine Julien
An ultrametric Cantor set can be seen as the boundary of a rooted weighted tree called the Michon tree. The notion of Assouad dimension is re-interpreted as seen on the Michon tree…
math.GN2010★ 1 cited
Embedding of self-similar ultrametric Cantor sets
A. Julien, J. Savinien
We study self-similar ultrametric Cantor sets arising from stationary Bratteli diagrams. We prove that such a Cantor set C is bi-Lipschitz embeddable in R^(d+1), where d denotes th…