Combinatorial and probabilistic properties of systems of numeration

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 K-G of N and the extension of the addition-by-one map tau on K-G (the 'odometer'). We give sufficient conditions for the existence and uniqueness of tau-invariant measures on K-G in terms of combinatorial properties of G.
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Guy Barat, Peter Grabner. Combinatorial and probabilistic properties of systems of numeration. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2016, 36 (02), pp.422 - 457. ⟨10.1017/etds.2014.69⟩. ⟨hal-01487856⟩

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