Generalization of a theorem of Kusmin

DOI10.1007/BF01305774zbMath0819.11028OpenAlexW2047948978MaRDI QIDQ1335534

Karma Dajani, Cornelis Kraaikamp

Publication date: 9 October 1994

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178657

zbMATH Keywords

probability density functiontransformationgeneralization of Gauss-Kuzmin theoremmap of unit-interval to itselfmetrical continued fractions

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55)

Related Items (6)

An application of the sub-additive ergodic theorem to the metric theory of continued fractions ⋮ The rate of convergence of approximations of a continued fraction ⋮ Two asymptotic distributions related to Rényi-type continued fraction expansions ⋮ A two-dimensional Gauss-Kuzmin theorem associated with the random Fibonacci-type sequences ⋮ On convergence rate in the Gauss-Kuzmin problem for \(\theta\)-expansions ⋮ A Gauss-Kusmin theorem for optimal continued fractions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The distribution of continued fraction approximations
• Metrical theory for a class of continued fraction transformations and their natural extensions
• Ein Gauss-Kusmin-Levy-Satz für Kettenbrüche nach nächsten Ganzen
• On symmetric and asymmetric diophantine approximation by continued fractions
• Some remarks on Kuzmin's theorem for F-expansions
• Über Einen Kusminschen Satz
• The metrical theory of continued fractions to the nearer integer
• On the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces
• Metrische Theorie einer Klasse zahlentheoretischer Transformationen
• On the ergodic theorems (II) (Ergodic theory of continued fractions)

This page was built for publication: Generalization of a theorem of Kusmin