Maximizing Bernoulli measures and dimension gaps for countable branched systems

S Baker; N Jurga

doi:10.1017/etds.2020.41

Maximizing Bernoulli measures and dimension gaps for countable branched systems

S Baker, N Jurga

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Kifer, Peres, and Weiss proved in [A dimension gap for continued fractionswith 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 thecontinued fraction expansion independent and identically distributed random variables. Inthis paper we prove that amongst this class of measures, there exists one whose dimensionis maximal. Our results also apply in the more general setting of countable branchedsystems

Original language	English
Pages (from-to)	1921-1939
Number of pages	19
Journal	Ergodic Theory and Dynamical Systems
Volume	41
Issue number	7
Early online date	26 May 2020
DOIs	https://doi.org/10.1017/etds.2020.41
Publication status	Published - Jul 2021

Keywords

Continued fractions
Bernoulli measures
Dimensions of measures

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10.1017/etds.2020.41

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title = "Maximizing Bernoulli measures and dimension gaps for countable branched systems",

abstract = "Kifer, Peres, and Weiss proved in [A dimension gap for continued fractionswith 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 thecontinued fraction expansion independent and identically distributed random variables. Inthis paper we prove that amongst this class of measures, there exists one whose dimensionis maximal. Our results also apply in the more general setting of countable branchedsystems",

keywords = "Continued fractions, Bernoulli measures, Dimensions of measures",

author = "S Baker and N Jurga",

note = "The first author was supported by EPSRC grant EP/M001903/1. Part of this work was completed whilst the authors were visiting the Mittag-Leffler Institute as part of the program {\textquoteleft}Fractal Geometry and Dynamics{\textquoteright}. ",

year = "2021",

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doi = "10.1017/etds.2020.41",

language = "English",

volume = "41",

pages = "1921--1939",

journal = "Ergodic Theory and Dynamical Systems",

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T1 - Maximizing Bernoulli measures and dimension gaps for countable branched systems

AU - Baker, S

AU - Jurga, N

N1 - The first author was supported by EPSRC grant EP/M001903/1. Part of this work was completed whilst the authors were visiting the Mittag-Leffler Institute as part of the program ‘Fractal Geometry and Dynamics’.

PY - 2021/7

Y1 - 2021/7

N2 - Kifer, Peres, and Weiss proved in [A dimension gap for continued fractionswith 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 thecontinued fraction expansion independent and identically distributed random variables. Inthis paper we prove that amongst this class of measures, there exists one whose dimensionis maximal. Our results also apply in the more general setting of countable branchedsystems

AB - Kifer, Peres, and Weiss proved in [A dimension gap for continued fractionswith 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 thecontinued fraction expansion independent and identically distributed random variables. Inthis paper we prove that amongst this class of measures, there exists one whose dimensionis maximal. Our results also apply in the more general setting of countable branchedsystems

KW - Continued fractions

KW - Bernoulli measures

KW - Dimensions of measures

U2 - 10.1017/etds.2020.41

DO - 10.1017/etds.2020.41

M3 - Article

SN - 0143-3857

VL - 41

SP - 1921

EP - 1939

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 7

ER -

Maximizing Bernoulli measures and dimension gaps for countable branched systems

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Keywords

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