TY - JOUR
T1 - Maximising Bernoulli measures and dimension gaps for countable branched systems
AU - Baker, Simon
AU - Jurga, Natalia
PY - 2020/5/26
Y1 - 2020/5/26
N2 - 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-c0 for 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.
AB - 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-c0 for 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.
KW - Bernoulli measures
KW - continued fractions
KW - dimensions of measures
UR - http://www.scopus.com/inward/record.url?scp=85085569638&partnerID=8YFLogxK
U2 - 10.1017/etds.2020.41
DO - 10.1017/etds.2020.41
M3 - Article
SN - 0143-3857
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
ER -