Topology of the set of univoque bases

DOI10.1016/j.topol.2016.01.023zbMath1362.11010OpenAlexW2268141055MaRDI QIDQ281764

Vilmos Komornik, Martijn de Vries, Paola Loreti

Publication date: 11 May 2016

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2016.01.023

zbMATH Keywords

Cantor setsgreedy expansionnon-integer basesbeta-expansionquasi-greedy expansionunique expansion

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Radix representation; digital problems (11A63) Symbolic dynamics (37B10) Metric theory of continued fractions (11K50)

Related Items

Univoque graphs for non-integer base expansions, Topology of univoque sets in real base expansions, Expansions in multiple bases over general alphabets, Algebraic sums and products of univoque bases, Univoque bases and Hausdorff dimension, A quasi-ergodic approach to non-integer base expansions, Metric results for numbers with multiple \(q\)-expansions, Univoque bases of real numbers: simply normal bases, irregular bases and multiple rationals, Bifurcations of digit frequencies in unique expansions, Intersection of Sierpinski gasket with its translation, Univoque bases of real numbers: local dimension, devil's staircase and isolated points, The -transformation with a hole at 0, Critical bases for ternary alphabets, Entropy, topological transitivity, and dimensional properties of unique 𝑞-expansions, Cantor type functions in non-integer bases, Expansions in multiple bases, Bases in which some numbers have exactly two expansions, Hausdorff dimension of multiple expansions, On the continuity of the Hausdorff dimension of the univoque set, Hausdorff dimension of frequency sets of univoque sequences, How inhomogeneous Cantor sets can pass a point, Relative bifurcation sets and the local dimension of univoque bases, On the specification property and synchronization of uniqueq-expansions, Expansions of generalized Thue-Morse numbers

Cites Work

• Generalized golden ratios of ternary alphabets
• On the topological structure of univoque sets
• Invariant densities for random \(\beta\)-expansions
• A property of algebraic univoque numbers
• Unique expansions of real numbers
• On the uniqueness of the expansions \(1=\sum q^{-n_i}\)
• Subexpansions, superexpansions and uniqueness properties in non-integer bases
• Unique infinite expansions in noninteger bases
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• Unique Developments in Non-Integer Bases
• Random \beta-expansions
• Almost Every Number Has a Continuum of b-Expansions
• Generalised golden ratios over integer alphabets
• Hausdorff dimension of unique beta expansions
• Characterization of the unique expansions $1=\sum^{\infty}_{i=1}q^{-n_ i}$ and related problems
• Unique representations of real numbers in non-integer bases
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