A canonical thickening of ℚ and the entropy ofα-continued fraction transformations

DOI10.1017/S0143385711000447zbMath1268.37040arXiv1004.3790MaRDI QIDQ3166352

Carlo Carminati, Giulio Tiozzo

Publication date: 11 October 2012

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.3790

zbMATH Keywords

entropycontinued fraction transformationscanonical thickening

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Dynamical systems involving maps of the interval (37E05) Metric theory of continued fractions (11K50)

Related Items (13)

An entropy problem of the \(\alpha \)-continued fraction maps ⋮ Invariant measures for continued fraction algorithms with finitely many digits ⋮ The bifurcation locus for numbers of bounded type ⋮ Natural extensions and entropy of \(\alpha \)-continued fraction expansion maps with odd partial quotients ⋮ Matching for a family of infinite measure continued fraction transformations ⋮ Hausdorff dimensions of perturbations of a conformal iterated function system via thermodynamic formalism ⋮ 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 ⋮ Topological entropy of quadratic polynomials and dimension of sections of the Mandelbrot set ⋮ Tanaka–Ito α-continued fractions and matching

Cites Work

• Metrical theory for a class of continued fraction transformations and their natural extensions
• Continued fractions and Brjuno functions
• Critical circle maps near bifurcation
• The entropy of α-continued fractions: numerical results
• The non-monotonicity of the entropy of α-continued fraction transformations
• Dynamical analysis of α-Euclidean algorithms

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