A natural extension for the greedy \(\beta\)-transformation with three arbitrary digits

DOI10.1007/s10474-009-8212-0zbMath1212.37001OpenAlexW2098106291MaRDI QIDQ987583

Charlene Kalle, Karma Dajani

Publication date: 13 August 2010

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://dspace.library.uu.nl/handle/1874/197282

zbMATH Keywords

absolutely continuous invariant measuregreedy expansionnatural expansion

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55)

Related Items (4)

Natural extensions for piecewise affine maps via Hofbauer towers ⋮ On the invariant density of the random \(\beta\)-transformation ⋮ Shrinking random \(\beta\)-transformation ⋮ Optimal expansions in non-integer bases

Cites Work

• Invariant densities for random \(\beta\)-expansions
• Invariant measures for piecewise linear transformations of the interval
• Random \(\beta\)-expansions with deleted digits
• The natural extension of the \(\beta\)-transformation
• Greedy expansions and sets with deleted digits
• Local dimensions for the random beta-transformation
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• Bounded variation and invariant measures
• Ergodic properties of a class of piecewise linear transformations
• Almost Every Number Has a Continuum of b-Expansions
• $\beta$-transformation, natural extension and invariant measure
• On the Morphology of γ-Expansions with Deleted Digits
• The Hausdorff Dimension of λ-Expansions with Deleted Digits

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