Entropy, topological transitivity, and dimensional properties of unique 𝑞-expansions

DOI10.1090/TRAN/7370zbMath1435.11016arXiv1609.02122OpenAlexW2963065385MaRDI QIDQ4645115

Rafael Alcaraz Barrera, Derong Kong, Simon Baker

Publication date: 10 January 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.02122

zbMATH Keywords

Hausdorff dimensiontopological transitivitybox dimensiontopological entropyexpansions in non-integer bases

Mathematics Subject Classification ID

Combinatorics on words (68R15) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Topological entropy (37B40) Radix representation; digital problems (11A63) Symbolic dynamics (37B10)

Related Items (22)

Density spectrum of Cantor measure ⋮ Expansions in multiple bases over general alphabets ⋮ The bifurcation locus for numbers of bounded type ⋮ A quasi-ergodic approach to non-integer base expansions ⋮ Metric results for numbers with multiple \(q\)-expansions ⋮ The Ruelle operator for symmetric \(\beta\)-shifts ⋮ Digit frequencies and self-affine sets with non-empty interior ⋮ Bifurcations of digit frequencies in unique expansions ⋮ Univoque bases of real numbers: local dimension, devil's staircase and isolated points ⋮ Multiple codings of self-similar sets with overlaps ⋮ Critical base for the unique codings of fat Sierpinski gasket ⋮ Non-uniform expansions of real numbers ⋮ Bifurcation sets arising from non-integer base expansions ⋮ Thue-Morse-Sturmian words and critical bases for ternary alphabets ⋮ Numbers with simply normal β-expansions ⋮ Hausdorff dimension of multiple expansions ⋮ On the continuity of the Hausdorff dimension of the univoque set ⋮ Arithmetic on self-similar sets ⋮ Relative bifurcation sets and the local dimension of univoque bases ⋮ On the specification property and synchronization of uniqueq-expansions ⋮ Hausdorff dimension of frequency sets in beta-expansions ⋮ RESONANCE BETWEEN SELF-SIMILAR SETS AND THEIR UNIVOQUE SETS

Cites Work

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