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Combinatorial and probabilistic properties of systems of numeration

  • GUY BARAT (a1) and PETER GRABNER (a2)
Abstract

Let $G=(G_{n})_{n}$ be a strictly increasing sequence of positive integers with $G_{0}=1$ . We study the system of numeration defined by this sequence by looking at the corresponding compactification ${\mathcal{K}}_{G}$ of $\mathbb{N}$ and the extension of the addition-by-one map ${\it\tau}$ on ${\mathcal{K}}_{G}$ (the ‘odometer’). We give sufficient conditions for the existence and uniqueness of ${\it\tau}$ -invariant measures on ${\mathcal{K}}_{G}$ in terms of combinatorial properties of $G$ .

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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