On a family of continued fraction transformations and their ergodic properties

DOI10.3836/tjm/1270215745zbMath0464.10038OpenAlexW2038211851MaRDI QIDQ1153943

Shigeru Tanaka, Shunji Ito

Publication date: 1981

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3836/tjm/1270215745

zbMATH Keywords

endomorphismrate of approximationdensity function of invariant measureergodic properties changesone-parameter family of continued fraction expansions

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16)

Related Items (14)

Ergodicity of Iwasawa continued fractions via markable hyperbolic geodesics ⋮ On the ergodic theory of Tanaka-Ito type \(\alpha \)-continued fractions ⋮ An entropy problem of the \(\alpha \)-continued fraction maps ⋮ Natural extensions and entropy of \(\alpha \)-continued fraction expansion maps with odd partial quotients ⋮ Regularity properties of \(k\)-Brjuno and Wilton functions ⋮ Convergence of improper Iwasawa continued fractions ⋮ Complex continued fractions: early work of the brothers Adolf and Julius Hurwitz ⋮ Purely periodic and transcendental complex continued fractions ⋮ The Hausdorff dimension spectrum of conformal graph directed Markov systems and applications to nearest integer continued fractions ⋮ Ergodicity of \(N\)-continued fraction expansions ⋮ Description of Generalized Continued Fractions by Finite Automata ⋮ Metrical theory for \(\alpha \)-Rosen fractions ⋮ Tanaka–Ito α-continued fractions and matching ⋮ Matching for random systems with an application to minimal weight expansions

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