Lipschitz equivalence of graph-directed fractals

Ying Xiong; Lifeng Xi

Ying Xiong ; Lifeng Xi

Studia Mathematica, Tome 192 (2009), p. 197-205 / Harvested from The Polish Digital Mathematics Library

Résumé

This paper studies the geometric structure of graph-directed sets from the point of view of Lipschitz equivalence. It is proved that if ${E_{i}}_{i}$ and ${F_{j}}_{j}$ are dust-like graph-directed sets satisfying the transitivity condition, then $E_{i ₁}$ and $E_{i ₂}$ are Lipschitz equivalent, and $E_{i}$ and $F_{j}$ are quasi-Lipschitz equivalent when they have the same Hausdorff dimension.

Publié le : 2009-01-01

Zbl 1178.28020

EUDML-ID : urn:eudml:doc:284465

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     title = {Lipschitz equivalence of graph-directed fractals},
     journal = {Studia Mathematica},
     volume = {192},
     year = {2009},
     pages = {197-205},
     zbl = {1178.28020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-2-6}
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Ying Xiong; Lifeng Xi. Lipschitz equivalence of graph-directed fractals. Studia Mathematica, Tome 192 (2009) pp. 197-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-2-6/