Let K ⊆ ℝ be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence, we can show that the set of points with a unique coding is a graph-directed self-similar set in the sense of Mauldin and Williams (1988). The theory of Mauldin and Williams then provides a method by which we can explicitly calculate the Hausdorff dimension of this set. Our algorithm can be applied generically, and our result generalises the work of Daróczy, Kátai, Kallós, Komornik and de Vries.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-3-4,
author = {Simon Baker and Karma Dajani and Kan Jiang},
title = {On univoque points for self-similar sets},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {265-282},
zbl = {06390222},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-3-4}
}
Simon Baker; Karma Dajani; Kan Jiang. On univoque points for self-similar sets. Fundamenta Mathematicae, Tome 228 (2015) pp. 265-282. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-3-4/