On univoque points for self-similar sets

Simon Baker, Karma Dajani, and Kan Jiang. "On univoque points for self-similar sets." Fundamenta Mathematicae 228.3 (2015): 265-282. <http://eudml.org/doc/286110>.

@article{SimonBaker2015,
abstract = {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.},
author = {Simon Baker, Karma Dajani, Kan Jiang},
journal = {Fundamenta Mathematicae},
keywords = {univoque set; self-similar sets; hausdorff dimension},
language = {eng},
number = {3},
pages = {265-282},
title = {On univoque points for self-similar sets},
url = {http://eudml.org/doc/286110},
volume = {228},
year = {2015},
}

TY - JOUR
AU - Simon Baker
AU - Karma Dajani
AU - Kan Jiang
TI - On univoque points for self-similar sets
JO - Fundamenta Mathematicae
PY - 2015
VL - 228
IS - 3
SP - 265
EP - 282
AB - 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.
LA - eng
KW - univoque set; self-similar sets; hausdorff dimension
UR - http://eudml.org/doc/286110
ER -