The quality of the diophantine approximations found by the Jacobi--Perron algorithm and related algorithms

DOI10.1007/BF01667310zbMath0790.11059OpenAlexW2316412685MaRDI QIDQ688961

Jeffrey C. Lagarias

Publication date: 26 June 1994

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178612

zbMATH Keywords

Oseledec's multiplicative ergodic theorembest approximation exponentMarkovian multivariate continued fractionmultivariate continued fractionsimplex splitting multivariate continued fractionuniform approximation exponent

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Metric theory of continued fractions (11K50)

Related Items (26)

EXPONENTIALLY STRONG CONVERGENCE OF NON-CLASSICAL MULTIDIMENSIONAL CONTINUED FRACTION ALGORITHMS ⋮ Thed-Dimensional Gauss Transformation: Strong Convergence and Lyapunov Exponents ⋮ The Three-Dimensional Gauss Algorithm Is Strongly Convergent Almost Everywhere ⋮ Multi-dimensional maps with infinite invariant measures and countable state sofic shifts ⋮ A generalized family of multidimensional continued fractions: TRIP Maps ⋮ Convergence of continued fraction type algorithms and generators ⋮ Simplicity of spectra for certain multidimensional continued fraction algorithms ⋮ The Brun gcd algorithm in high dimensions is almost always subtractive ⋮ The convergence of the generalised Selmer algorithm ⋮ Dynamics of Ostrowski skew-product: 1. Limit laws and Hausdorff dimensions ⋮ Multidimensional continued fractions and symbolic codings of toral translations ⋮ Cubic irrationals and periodicity via a family of multi-dimensional continued fraction algorithms ⋮ Geometry, dynamics, and arithmetic of $S$-adic shifts ⋮ On integer partitions and continued fraction type algorithms ⋮ Periodic Jacobi-Perron expansions associated with a unit ⋮ A Note on Lyapunov Theory for Brun Algorithm ⋮ Some Monoids of Pisot Matrices ⋮ What do continued fractions accomplish? ⋮ On the second Lyapunov exponent of some multidimensional continued fraction algorithms ⋮ Simultaneous approximations to \(p\)-adic numbers and algebraic dependence via multidimensional continued fractions ⋮ 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) ⋮ A multidimensional continued fraction based on a high-order recurrence relation ⋮ Numerical Study of Invariant Sets of a Quasiperiodic Perturbation of a Symplectic Map ⋮ Generalizing the Minkowski question mark function to a family of multidimensional continued fractions ⋮ Bispecial Factors in the Brun S-Adic System ⋮ Almost everywhere balanced sequences of complexity \(2n + 1\)

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• The Jacobi-Perron algorithm its theory and application
• Ergodic Properties of Linear Dynamical Systems
• Ein Kuzminscher Satz über den Jacobischen Algorithmus.
• Dirichlet's theorem on diophantine approximation. II

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