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)
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Publication:5936663
DOI10.5802/aif.1832zbMath1012.11060OpenAlexW2324299322MaRDI QIDQ5936663
Yves Guivarc'h, Anne Broise-Alamichel
Publication date: 4 July 2001
Published in: Annales de l'Institut Fourier (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=AIF_2001__51_3_565_0
periodic pointsLyapunov spectrumalmost everywhere exponential convergenceBrun algorithmJacobi-Perron algorithmmultidimensional continued fraction algorithmsproduct of random stationary matricessimplicity of the spectrumsimultaneous approximation of two realstransfer operators
Continued fractions and generalizations (11J70) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Simultaneous homogeneous approximation, linear forms (11J13) Metric theory of continued fractions (11K50)
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Cites Work
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- A proof of Oseledec's multiplicative ergodic theorem
- The quality of the diophantine approximations found by the Jacobi--Perron algorithm and related algorithms
- Approach to equilibrium for locally expanding maps in \({\mathbb{R}}^ k\)
- Propriétés de contraction d'un semi-groupe de matrices inversibles. Coefficients de Liapunoff d'un produit de matrices aléatoires indépendantes. (Contraction properties of a semigoup of invertible matrices. Lyapunov coefficient of a product of independent random matrices)
- A multidimensional continued fraction and some of its statistical properties
- A convergence exponent for multidimensional continued-fraction algorithms
- Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents
- Régularité du plus grand exposant caractéristique des produits de matrices aléatoires indépendantes et applications. (Regularity of the largest characteristic exponent of products of independent random matrices and applications)
- The metrical theory of Jacobi-Perron algorithm
- The three-dimensional Poincaré continued fraction algorithm
- Zariski closure and the dimension of the Gaussian law of the product of random matrices. I
- Théorie ergodique pour des classes d'opérations non completement continues
- Almost everywhere exponential convergence of the modified Jacobi—Perron algorithm
- Produits de matrices aléatoires et applications aux propriétés géometriques des sous-groupes du groupe linéaire
- Frontière de furstenberg, propriétés de contraction et théorèmes de convergence
- Propriétés ergodiques, en mesure infinie, de certains systèmes dynamiques fibrés
- A simple proof of the exponential convergence of the modified Jacobi–Perron algorithm
- Sums of Stationary Sequences Cannot Grow Slower Than Linearly
- Recurrence of Co-Cycles and Random Walks
- Mesures de Gauss pour des algorithmes de fractions continues multidimensionnelles
- Geodesic Multidimensional Continued Fractions
- On almost everywhere strong convergence of multi-dimensional continued fraction algorithms
- Fractions continues multidimensionnelles et lois stables
- Fonctions harmoniques pour un opérateur de transition et applications
- On almost everywhere exponential convergence of the modified Jacobi-Perron algorithm: a corrected proof
- Noncommuting Random Products
- Continued fractions and the \(d\)-dimensional Gauss transformation
