The three-dimensional Poincaré continued fraction algorithm
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Publication:1895086
DOI10.1007/BF02783221zbMath0840.11030MaRDI QIDQ1895086
Publication date: 14 August 1995
Published in: Israel Journal of Mathematics (Search for Journal in Brave)
Ergodic theory (37A99) Metric theory of continued fractions (11K50) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)
Related Items (24)
Multidimensional Farey partitions ⋮ Ergodic properties of triangle partitions ⋮ Simplex-karyon algorithm of multidimensional continued fraction expansion ⋮ Periodic karyon expansions of algebraic units in multidimensional continued fractions ⋮ The convergence of the generalised Selmer algorithm ⋮ The best approximation of algebraic numbers by multidimensional continued fractions ⋮ A local algorithm for constructing derived tilings of the two-dimensional torus ⋮ The mathematical research of William Parry FRS ⋮ Factor complexity of \(S\)-adic words generated by the Arnoux-Rauzy-Poincaré algorithm ⋮ Exactness of the Euclidean algorithm and of the Rauzy induction on the space of interval exchange transformations ⋮ 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 ⋮ Asymptotics for two-dimensional Farey-Brocot nets ⋮ 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) ⋮ The karyon algorithm for expansion in multidimensional continued fractions ⋮ Absorbing sets of homogeneous subtractive algorithms ⋮ Analysis of generalized continued fraction algorithms over polynomials ⋮ A 2-DIMENSIONAL ALGORITHM RELATED TO THE FAREY–BROCOT SEQUENCE ⋮ Continued fractions on the Veech surfaces ⋮ Lebesgue Ergodicity of a Dissipative Subtractive Algorithm ⋮ Almost everywhere balanced sequences of complexity \(2n + 1\) ⋮ The Borel-Bernstein theorem for multidimensional continued fractions ⋮ Orbit distribution on \(\mathbb R^2\) under the natural action of \(\mathrm{SL}(2,\mathbb Z)\)
Cites Work
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- Lectures on number theory. Ed. by Nikolaos Kritikos. Transl. from the German, with some additional material, by William C. Schulz
- Ergodic properties of some permutation processes
- On the Parry-Daniels Transformation
- Mesures de Gauss pour des algorithmes de fractions continues multidimensionnelles
- Ranks and measures
- Processes generating permutation expansions
- A Metrically Transitive Group Defined by the Modular Groups
- Interval exchange transformations
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