Almost everywhere exponential convergence of the modified Jacobi—Perron algorithm

DOI10.1017/S0143385700007380zbMath0846.28005OpenAlexW1998694370MaRDI QIDQ3140464

Shunji Ito, Makoto Ohtsuki, Michael S. Keane

Publication date: 23 September 1996

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

Full work available at URL: https://doi.org/10.1017/s0143385700007380

zbMATH Keywords

simultaneous approximationJacobi-Perron algorithmergodic transformation

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55)

Related Items (9)

On almost everywhere exponential convergence of the modified Jacobi-Perron algorithm: a corrected proof ⋮ EXPONENTIALLY STRONG CONVERGENCE OF NON-CLASSICAL MULTIDIMENSIONAL CONTINUED FRACTION ALGORITHMS ⋮ Convergence of continued fraction type algorithms and generators ⋮ Levels of multi-continued fraction expansion of multi-formal Laurent series ⋮ The modified Jacobi-Perron algorithm over \(\mathbb F_q (X)^d\) ⋮ On the second Lyapunov exponent of some multidimensional continued fraction algorithms ⋮ A conversion algorithm based on the technique of singularization ⋮ 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) ⋮ Existence, mixing and approximation of invariant densities for expanding maps on \(\mathbb{R}^r\)

Cites Work

• Unnamed Item
• A simple proof of some ergodic theorems
• Invariant measures for maps of continued fraction type
• A multidimensional continued fraction and some of its statistical properties
• A convergence exponent for multidimensional continued-fraction algorithms

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