Maximising Bernoulli measures and dimension gaps for countable branched systems

Simon Baker, Natalia Jurga

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Abstract

Kifer, Peres, and Weiss proved in [A dimension gap for continued fractions with independent digits. Israel J. Math.124 (2001), 61–76] that there exists c0 > 0, such that dim μ ≤ 1-cfor any probability measure μ, which makes the digits of the continued fraction expansion independent and identically distributed 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.
Original languageEnglish
JournalErgodic Theory and Dynamical Systems
DOIs
Publication statusPublished - 26 May 2020

Keywords

  • Bernoulli measures
  • continued fractions
  • dimensions of measures

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