Lipschitz equivalence of graph-directed fractals

Ying Xiong, and Lifeng Xi. "Lipschitz equivalence of graph-directed fractals." Studia Mathematica 194.2 (2009): 197-205. <http://eudml.org/doc/284465>.

@article{YingXiong2009,
abstract = {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 $E_\{i₁\}$ and $E_\{i₂\}$ are Lipschitz equivalent, and $E_\{i\}$ and $F_\{j\}$ are quasi-Lipschitz equivalent when they have the same Hausdorff dimension.},
author = {Ying Xiong, Lifeng Xi},
journal = {Studia Mathematica},
keywords = {fractal; graph-directed sets; Lipschitz equivalence; quasi-Lipschitz equivalence},
language = {eng},
number = {2},
pages = {197-205},
title = {Lipschitz equivalence of graph-directed fractals},
url = {http://eudml.org/doc/284465},
volume = {194},
year = {2009},
}

TY - JOUR
AU - Ying Xiong
AU - Lifeng Xi
TI - Lipschitz equivalence of graph-directed fractals
JO - Studia Mathematica
PY - 2009
VL - 194
IS - 2
SP - 197
EP - 205
AB - 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 $E_{i₁}$ and $E_{i₂}$ are Lipschitz equivalent, and $E_{i}$ and $F_{j}$ are quasi-Lipschitz equivalent when they have the same Hausdorff dimension.
LA - eng
KW - fractal; graph-directed sets; Lipschitz equivalence; quasi-Lipschitz equivalence
UR - http://eudml.org/doc/284465
ER -