On some symmetric multidimensional continued fraction algorithms

DOI10.1017/etds.2016.112zbMath1403.37089arXiv1508.07814OpenAlexW2262768638MaRDI QIDQ3176213

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Publication date: 19 July 2018

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

Full work available at URL: https://arxiv.org/abs/1508.07814

zbMATH Keywords

Brun algorithmfractal boundarycontinued fraction algorithmCassaigne algorithmreverse algorithm

Mathematics Subject Classification ID

Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items (14)

On the dimension group of unimodular \(\mathcal{S}\)-adic subshifts ⋮ Simplicity of spectra for certain multidimensional continued fraction algorithms ⋮ Periodic karyon expansions of algebraic units in multidimensional continued fractions ⋮ Multidimensional continued fractions and symbolic codings of toral translations ⋮ Generalizations of Sturmian sequences associated with \(\boldsymbol{N}\)-continued fraction algorithms ⋮ The best approximation of algebraic numbers by multidimensional continued fractions ⋮ A local algorithm for constructing derived tilings of the two-dimensional torus ⋮ S-adic Sequences: A Bridge Between Dynamics, Arithmetic, and Geometry ⋮ On the second Lyapunov exponent of some multidimensional continued fraction algorithms ⋮ Linear-fractional invariance of multidimensional continued fractions ⋮ Linear-fractional invariance of the simplex-module algorithm for expanding algebraic numbers in multidimensional continued fractions ⋮ Localized Pisot matrices and joint approximations of algebraic numbers ⋮ The karyon algorithm for expansion in multidimensional continued fractions ⋮ Almost everywhere balanced sequences of complexity \(2n + 1\)

Cites Work

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• Factor complexity of \(S\)-adic words generated by the Arnoux-Rauzy-Poincaré algorithm
• Gauss measures for transformations on the space of interval exchange maps
• Natural extensions and entropy ofα-continued fractions
• Mesures de Gauss pour des algorithmes de fractions continues multidimensionnelles
• The Rauzy Gasket
• Exposants caractéristiques de l'algorithme de Jacobi-Perron et de la transformation associée. (Characteristic exponents of the Jacobi-Perron algorithm and of the associated map)
• Continued fractions and the \(d\)-dimensional Gauss transformation

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