On univoque points for self-similar sets

• Autorzy: Simon Baker , Karma Dajani , Kan Jiang
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37C45: Dimension theory of dynamical systems
• 37A45: Relations with number theory and harmonic analysis

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 228
• Numer: 3
• Strony: 265-282

Daty

wydano

2015

Twórcy

autor

Simon Baker

• School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK

autor

Karma Dajani

• Department of Mathematics, Utrecht University, Budapestlaan 6, 3508TA Utrecht, The Netherlands

autor

Kan Jiang

• Department of Mathematics, Utrecht University, Budapestlaan 6, 3508TA Utrecht, The Netherlands

Identyfikatory

DOI

10.4064/fm228-3-4