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 : 10.5802/aif.1832
Classification : 11J70, 37H15
Mot clés : spectre de Lyapunov, algorithme de Jacobi-Perron, produit de matrices aléatoires stationnaires, points périodiques, opérateurs de transfert
Keywords: Lyapunov spectrum, Jacobi-Perron algorithm, product of stationary random matrices, periodic points, transfer operators
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. http://archive.numdam.org/articles/10.5802/aif.1832/

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