Combinatorial and probabilistic properties of systems of numeration
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.