Separation properties for self-conformal sets

Yuan-Ling Ye

Yuan-Ling Ye

Studia Mathematica, Tome 151 (2002), p. 33-44 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $0 < ℋ^{α} (K) < \infty$ . We give a simple proof of this result as well as discuss some further properties related to the separation condition.

Publié le : 2002-01-01

Zbl 1034.28005

EUDML-ID : urn:eudml:doc:285301

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     title = {Separation properties for self-conformal sets},
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     volume = {151},
     year = {2002},
     pages = {33-44},
     zbl = {1034.28005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm152-1-3}
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Yuan-Ling Ye. Separation properties for self-conformal sets. Studia Mathematica, Tome 151 (2002) pp. 33-44. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm152-1-3/