The Borel-Bernstein theorem for multidimensional continued fractions

DOI10.1007/BF02788074zbMath1015.11039OpenAlexW2169029961MaRDI QIDQ1604965

Arnaldo Nogueira

Publication date: 10 July 2002

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02788074

zbMATH Keywords

Jacobi-Perron algorithminterval exchange transformationsFarey fractionsPoincaré algorithmmultidimensional continued fraction expansionsBorel-Bernstein theoremmetric theory of regular continued fractionsrecurrent multidimensional continued fraction algorithms

Mathematics Subject Classification ID

Topological dynamics (37B99) Strong limit theorems (60F15) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Metric theory of continued fractions (11K50)

Related Items (4)

Multidimensional Farey partitions ⋮ Exactness of the Euclidean algorithm and of the Rauzy induction on the space of interval exchange transformations ⋮ A complex Borel-Bernstein theorem ⋮ Continued fractions on the Veech surfaces

Cites Work

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• Gauss measures for transformations on the space of interval exchange maps
• Interval exchange transformations and measured foliations
• The metrical theory of Jacobi-Perron algorithm
• The three-dimensional Poincaré continued fraction algorithm
• Metrische Sätze über den Jacobischen Algorithmus
• Échanges d'intervalles et transformations induites
• Measured foliations on nonorientable surfaces
• Ergodic properties of some permutation processes
• Simplicial systems for interval exchange maps and measured foliations
• The Metric Theory of Interval Exchange Transformations II. Approximation by Primitive Interval Exchanges
• On the Parry-Daniels Transformation
• Mesures de Gauss pour des algorithmes de fractions continues multidimensionnelles
• Geodesic Multidimensional Continued Fractions
• Topological weak-mixing of interval exchange maps
• Interval exchange transformations

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