IP-Dirichlet measures and IP-rigid dynamical systems: an approach via generalized Riesz products

2012/09/13 by Sophie Grivaux, Grivaux, Sophie
Mathematics · #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CA #math.DS

paper · pdf · doi:10.48550/arxiv.1209.2884

arxiv created 2012/09/13 · arxiv updated 2012/09/14

Abstract

If (n_k)_{k≥ 1} is a strictly increasing sequence of integers, a continuous probability measure σ on the unit circle \mathbbT is said to be IP-Dirichlet with respect to (n_k)_{k≥ 1} if σ(∑_{k∈ F}n_k)→ 1 as F runs over all non-empty finite subsets F of ℕ and the minimum of F tends to infinity. IP-Dirichlet measures and their connections with IP-rigid dynamical systems have been investigated recently by Aaronson, Hosseini and Lemańczyk. We simplify and generalize some of their results, using an approach involving generalized Riesz products.

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