The non-monotonicity of the entropy of α-continued fraction transformations

DOI10.1088/0951-7715/21/6/003zbMath1143.11024OpenAlexW1991556085MaRDI QIDQ3507959

Rie Natsui, Hitoshi Nakada

Publication date: 24 June 2008

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/21/6/003

zbMATH Keywords

natural extension\(\alpha\)-continued fractionsentropy of one-dimensional maps

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Metric theory of continued fractions (11K50) Dynamical systems involving one-parameter continuous families of measure-preserving transformations (37A10)

Related Items (14)

A canonical thickening of ℚ and the entropy ofα-continued fraction transformations ⋮ 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 \(g^2\) ⋮ Natural extensions and entropy of \(\alpha \)-continued fraction expansion maps with odd partial quotients ⋮ Matching for a family of infinite measure continued fraction transformations ⋮ Invariant measures, matching and the frequency of 0 for signed binary expansions ⋮ Continued fractions with $SL(2, Z)$-branches: combinatorics and entropy ⋮ Matching for generalised \(\beta\)-transformations ⋮ Matching in a family of piecewise affine maps ⋮ On the equivalence relations of \(\alpha\)-continued fractions ⋮ Natural extensions for \(\alpha \)-Rosen continued fractions ⋮ Tanaka–Ito α-continued fractions and matching ⋮ Matching for random systems with an application to minimal weight expansions

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