Invariant densities for random continued fractions

Charlene Kalle; Valentin Matache; Masato Tsujii; Evgeny Verbitskiy

doi:10.1016/j.jmaa.2022.126163

Invariant densities for random continued fractions

Charlene Kalle, Valentin Matache, Masato Tsujii, Evgeny Verbitskiy

Mathematics

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

6 Scopus citations

Abstract

We continue the study of random continued fraction expansions, generated by random application of the Gauss and the Rényi backward continued fraction maps. We show that this random dynamical system admits a unique absolutely continuous invariant measure with smooth density.

Original language	English (US)
Article number	126163
Journal	Journal of Mathematical Analysis and Applications
Volume	512
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2022.126163
State	Published - Aug 15 2022

Keywords

Intermittent dynamics
Invariant measures
Nuclearity
Quasi-compactness
Random dynamics
Transfer operator

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2022.126163

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title = "Invariant densities for random continued fractions",

abstract = "We continue the study of random continued fraction expansions, generated by random application of the Gauss and the R{\'e}nyi backward continued fraction maps. We show that this random dynamical system admits a unique absolutely continuous invariant measure with smooth density.",

keywords = "Intermittent dynamics, Invariant measures, Nuclearity, Quasi-compactness, Random dynamics, Transfer operator",

author = "Charlene Kalle and Valentin Matache and Masato Tsujii and Evgeny Verbitskiy",

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year = "2022",

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AU - Kalle, Charlene

AU - Matache, Valentin

AU - Tsujii, Masato

AU - Verbitskiy, Evgeny

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Y1 - 2022/8/15

N2 - We continue the study of random continued fraction expansions, generated by random application of the Gauss and the Rényi backward continued fraction maps. We show that this random dynamical system admits a unique absolutely continuous invariant measure with smooth density.

AB - We continue the study of random continued fraction expansions, generated by random application of the Gauss and the Rényi backward continued fraction maps. We show that this random dynamical system admits a unique absolutely continuous invariant measure with smooth density.

KW - Intermittent dynamics

KW - Invariant measures

KW - Nuclearity

KW - Quasi-compactness

KW - Random dynamics

KW - Transfer operator

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JO - Journal of Mathematical Analysis and Applications

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Invariant densities for random continued fractions

Abstract

Keywords

ASJC Scopus subject areas

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