English

Maximising Bernoulli measures and dimension gaps for countable branched systems

Dynamical Systems 2018-02-22 v1

Abstract

Kifer, Peres, and Weiss proved that there exists c0>0,c_0>0, such that dimμ1c0\dim \mu\leq 1-c_0 for any probability measure μ\mu which makes the digits of the continued fraction expansion i.i.d. random variables. In this paper we prove that amongst this class of measures, there exists one whose dimension is maximal. Our results also apply in the more general setting of countable branched systems.

Keywords

Cite

@article{arxiv.1802.07585,
  title  = {Maximising Bernoulli measures and dimension gaps for countable branched systems},
  author = {Simon Baker and Natalia Jurga},
  journal= {arXiv preprint arXiv:1802.07585},
  year   = {2018}
}
R2 v1 2026-06-23T00:28:51.637Z