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

Broise-Alamichel, Anne; Guivarc'h, Yves

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.

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

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