Separation properties for self-conformal sets

Yuan-Ling Ye. "Separation properties for self-conformal sets." Studia Mathematica 152.1 (2002): 33-44. <http://eudml.org/doc/285301>.

@article{Yuan2002,
abstract = {For a one-to-one self-conformal contractive system $\{w_\{j\}\}_\{j=1\}^\{m\}$ on $ℝ^\{d\}$ with attractor K and conformality dimension α, Peres et al. showed that the open set condition and strong open set condition are both equivalent to $0 < ℋ^\{α\}(K) < ∞$. We give a simple proof of this result as well as discuss some further properties related to the separation condition.},
author = {Yuan-Ling Ye},
journal = {Studia Mathematica},
keywords = {self-conformal sets; open set condition; Hausdorff dimension; strong open set condition},
language = {eng},
number = {1},
pages = {33-44},
title = {Separation properties for self-conformal sets},
url = {http://eudml.org/doc/285301},
volume = {152},
year = {2002},
}

TY - JOUR
AU - Yuan-Ling Ye
TI - Separation properties for self-conformal sets
JO - Studia Mathematica
PY - 2002
VL - 152
IS - 1
SP - 33
EP - 44
AB - For a one-to-one self-conformal contractive system ${w_{j}}_{j=1}^{m}$ on $ℝ^{d}$ with attractor K and conformality dimension α, Peres et al. showed that the open set condition and strong open set condition are both equivalent to $0 < ℋ^{α}(K) < ∞$. We give a simple proof of this result as well as discuss some further properties related to the separation condition.
LA - eng
KW - self-conformal sets; open set condition; Hausdorff dimension; strong open set condition
UR - http://eudml.org/doc/285301
ER -