Exposants caractéristiques de l’algorithme de Jacobi-Perron et de la transformation associée
Annales de l'Institut Fourier, Tome 51 (2001) no. 3, pp. 565-686.

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.

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{\textquoteright}algorithme de {Jacobi-Perron} et de la transformation associ\'ee},
     journal = {Annales de l'Institut Fourier},
     pages = {565--686},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {51},
     number = {3},
     year = {2001},
     doi = {10.5802/aif.1832},
     zbl = {1012.11060},
     language = {fr},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1832/}
}
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) no. 3, pp. 565-686. doi : 10.5802/aif.1832. https://aif.centre-mersenne.org/articles/10.5802/aif.1832/

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