Invariant densities for random continued fractions

Invariant densities for random continued fractions

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.

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Veröffentlicht in:Journal of mathematical analysis and applications 2022-08, Vol.512 (2), p.126163, Article 126163
Hauptverfasser: Kalle, Charlene, Matache, Valentin, Tsujii, Masato, Verbitskiy, Evgeny
Format: Artikel
Sprache:eng
Schlagworte:
Intermittent dynamics
Invariant measures
Nuclearity
Quasi-compactness
Random dynamics
Transfer operator
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Beschreibung
Zusammenfassung: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2022.126163