The natural extension of the \(\beta\)-transformation

DOI10.1007/BF00058946zbMath0931.28014MaRDI QIDQ1297780

B. M. Solomyak, Cornelis Kraaikamp, Karma Dajani

Publication date: 14 September 1999

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

zbMATH Keywords

natural extension\(\beta\)-transformationBernoulli automorphismweakly-mixing

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) General theory of distribution modulo (1) (11K06)

Related Items

Dynamical directions in numeration ⋮ The natural extension of the random beta-transformation ⋮ Natural extensions for piecewise affine maps via Hofbauer towers ⋮ On the invariant density of the random \(\beta\)-transformation ⋮ On approximation by Lüroth series ⋮ A natural extension for the greedy \(\beta\)-transformation with three arbitrary digits ⋮ Skew product Smale endomorphisms over countable shifts of finite type ⋮ Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions ⋮ Ergodic properties of the Erdős measure, the entropy of the goldenshift, and related problems ⋮ Mixing properties of (α,β)-expansions ⋮ Smale endomorphisms over graph-directed Markov systems ⋮ Natural extensions for \(p\)-adic \(\beta\)-shifts and other scaling maps

Cites Work

• Unnamed Item
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• A construction of transversal flows for maximal Markov automorphisms
• \(\beta\)-expansions and symbolic dynamics
• On isomorphism of weak Bernoulli transformations
• β-automorphisms are Bernoulli shifts
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• Ergodic properties of a class of piecewise linear transformations
• Ergodic properties of generalized Lüroth series
• On induced transformations of Bernoulli shifts