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
Broise-Alamichel, Anne 1 ; Guivarc'h, Yves 2

1. Université Paris-Sud, UMR 8628 du CNRS, Laboratoire de Mathématiques, Équipe de Topologie et Dynamique, Bâtiment 425, 91405 Orsay Cedex (France)
2. Université de Rennes I, UMR 6625 du CNRS, IRMAR, Campus de Beaulieu, 35042 Rennes Cedex (France)
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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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