On the bifurcation set of unique expansions

DOI10.4064/AA171212-11-7zbMath1441.11018arXiv1612.07982OpenAlexW2964124679WikidataQ128057074 ScholiaQ128057074MaRDI QIDQ5376589

Fan Lü, Wenxia Li, Derong Kong, Charlene Kalle

Publication date: 13 May 2019

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.07982

zbMATH Keywords

topological entropybifurcation setdevil's staircaseHausdorff dimensionsunivoque basesunivoque sets

Mathematics Subject Classification ID

Radix representation; digital problems (11A63) Symbolic dynamics (37B10) Hausdorff and packing measures (28A78)

Related Items (10)

Density spectrum of Cantor measure ⋮ The bifurcation locus for numbers of bounded type ⋮ Bifurcations of digit frequencies in unique expansions ⋮ Univoque bases of real numbers: local dimension, devil's staircase and isolated points ⋮ Expansions in multiple bases ⋮ On the continuity of the Hausdorff dimension of the univoque set ⋮ Relative bifurcation sets and the local dimension of univoque bases ⋮ On the specification property and synchronization of uniqueq-expansions ⋮ On the smallest base in which a number has a unique expansion ⋮ Expansions of generalized Thue-Morse numbers

Cites Work

• Hausdorff dimension of univoque sets and devil's staircase
• Non-integer bases, iteration of continuous real maps, and an arithmetic self-similar set
• Dynamics of continued fractions and kneading sequences of unimodal maps
• On the continuity of the Hausdorff dimension of the univoque set
• Unique representations of real numbers in non-integer bases
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