Exposants caractéristiques de l'algorithme de Jacobi-Perron et de la transformation associée

Broise-Alamichel, Anne; Guivarc'h, Yves

Broise-Alamichel, Anne ; Guivarc'h, Yves

Annales de l'Institut Fourier, Tome 51 (2001), p. 565-686 / Harvested from Numdam

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Résumé
Abstract

On montre que les exposants de Lyapunov de l’algorithme de Jacobi-Perron, en dimension $d$ quelconque, sont tous différents et que la somme des exposants extrêmes est strictement positive. En particulier, si $d = 2$ , le deuxième exposant est strictement négatif.

We prove that, for every dimension $d$ , the Lyapunov exponents of the Jacobi-Perron algorithm are all different, and that the sum of the extreme exponents is strictly positive. Especially, if $d = 2$ , the second exponent is strictly negative.

Publié le : 2001-01-01

Zbl 1012.11060 | 2 citations dans Numdam

DOI : https://doi.org/10.5802/aif.1832
Classification: 11J70, 37H15
Mots clés: spectre de Lyapunov, algorithme de Jacobi-Perron, produit de matrices aléatoires stationnaires, points périodiques, opérateurs de transfert

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     author = {Broise-Alamichel, Anne and Guivarc'h, Yves},
     title = {Exposants caract\'eristiques de l'algorithme de Jacobi-Perron et de la transformation associ\'ee},
     journal = {Annales de l'Institut Fourier},
     volume = {51},
     year = {2001},
     pages = {565-686},
     doi = {10.5802/aif.1832},
     zbl = {1012.11060},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_2001__51_3_565_0}
}

Broise-Alamichel, Anne; Guivarc'h, Yves. Exposants caractéristiques de l'algorithme de Jacobi-Perron et de la transformation associée. Annales de l'Institut Fourier, Tome 51 (2001) pp. 565-686. doi : 10.5802/aif.1832. http://gdmltest.u-ga.fr/item/AIF_2001__51_3_565_0/

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