Natural extensions for \(\alpha \)-Rosen continued fractions

DOI10.2969/jmsj/06220649zbMath1209.11078arXiv0905.4588OpenAlexW2012378286WikidataQ57388056 ScholiaQ57388056MaRDI QIDQ978500

Thomas A. Schmidt, Ionica Smeets, Cornelis Kraaikamp

Publication date: 24 June 2010

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.4588

zbMATH Keywords

entropynatural extensionsRosen fractions

Mathematics Subject Classification ID

Related Items (5)

An entropy problem of the \(\alpha \)-continued fraction maps ⋮ Invariant measures for continued fraction algorithms with finitely many digits ⋮ Natural extensions for Nakada's \(\alpha\)-expansions: descending from \(1\) to \(g^2\) ⋮ The random continued fraction transformation ⋮ Natural extensions and entropy of \(\alpha \)-continued fraction expansion maps with odd partial quotients

Cites Work

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• On the Lenstra constant associated to the Rosen continued fractions
• On the entropy of Japanese continued fractions
• Metrical theory for \(\alpha \)-Rosen fractions
• Metrical theory for a class of continued fraction transformations and their natural extensions
• Continued fractions and Brjuno functions
• A class of continued fractions associated with certain properly discontinuous groups
• The non-monotonicity of the entropy of α-continued fraction transformations
• Metric and arithmetic properties of mediant-Rosen maps
• Natural extensions for the Rosen fractions
• A new class of continued fraction expansions

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