English

Purity results for some arithmetically defined measures

Dynamical Systems 2022-05-16 v3 Number Theory

Abstract

We study measures that are obtained as push-forwards of measures of maximal entropy on sofic shifts under digital maps (xk)kNkNxkβk(x_k)_{k\in\mathbb{N}}\mapsto\sum_{k\in\mathbb{N}}x_k\beta^{-k}, where β>1\beta>1 is a Pisot number. We characterise the continuity of such measures in terms of the underlying automaton and show a purity result.

Keywords

Cite

@article{arxiv.1908.09023,
  title  = {Purity results for some arithmetically defined measures},
  author = {Peter J. Grabner},
  journal= {arXiv preprint arXiv:1908.09023},
  year   = {2022}
}
R2 v1 2026-06-23T10:55:35.609Z