Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices
Bonatti, Christian ; Gómez-Mont, Xavier ; Viana, Marcelo
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003), p. 579-624 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2003__20_4_579_0,
     author = {Bonatti, Christian and G\'omez-Mont, Xavier and Viana, Marcelo},
     title = {G\'en\'ericit\'e d'exposants de Lyapunov non-nuls pour des produits d\'eterministes de matrices},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {20},
     year = {2003},
     pages = {579-624},
     doi = {10.1016/S0294-1449(02)00019-7},
     mrnumber = {1981401},
     zbl = {1025.37018},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPC_2003__20_4_579_0}
}

Bonatti, Christian; Gómez-Mont, Xavier; Viana, Marcelo. Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) pp. 579-624. doi : 10.1016/S0294-1449(02)00019-7. http://gdmltest.u-ga.fr/item/AIHPC_2003__20_4_579_0/

[1] Anosov D., Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Inst. Math. 90 (1967). | MR 224110 | Zbl 0176.19101

[2] Babillot M., Ledrappier F., Geodesic paths and horocyclic flow on abelian covers, in: Lie Groups and Ergodic Theory (Mumbai 1996), Tata Inst. Fund. Res. Stud. Math., 14, 1998, pp. 1-32. | MR 1699356 | Zbl 0967.37020

[3] J. Bochi, Genericity of zero Lyapunov exponents, Ergodic Theory Dynamical Systems 22 (2002). | MR 1944399 | Zbl 1023.37006

[4] C. Bonatti, X. Gómez-Mont, R. Vila, The foliated geodesic flow of Ricatti equations, Pre-publication Dijon.

[5] C. Bonatti, X. Gómez-Mont, Sur le comportement statistique des feuilles de certains feuilletages holomorphes, Enseignement Mathématique 38 (2001). | MR 1929320 | Zbl 1010.37025

[6] Bowen R., Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973) 428-459. | MR 339281 | Zbl 0282.58009

[7] Bowen R., Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lect. Notes in Math., 470, Springer-Verlag, 1975. | MR 442989 | Zbl 0308.28010

[8] Bowen R., Ruelle D., The ergodic theory of Axiom A flows, Invent. Math. 29 (1975) 181-202. | MR 380889 | Zbl 0311.58010

[9] Brin Ya., Pesin Ya., Partially hyperbolic systems, Akad. Nauk SSSR 1 (1974) 170-212. | Zbl 0304.58017

[10] Furstenberg H., Noncommuting random products, Trans. Amer. Math. Soc. 108 (1963) 377-428. | MR 163345 | Zbl 0203.19102

[11] Guivarc'H Y., Raugi A., Products of random matrices : convergence theorems, Contemp. Math. 50 (1986) 31-54. | MR 841080 | Zbl 0592.60015

[12] Haydn N., Canonical product structure of equlibrium states, Rand. Comput. Dynam. 2 (1994) 79-96. | MR 1265227 | Zbl 0810.58030

[13] Hirsch M., Pugh C., Shub M., Invariant Manifolds, Lect. Notes in Math., 583, Springer-Verlag, 1977. | MR 501173 | Zbl 0355.58009

[14] Hopf E., Ergodic theory and the geodesic flow on surfaces on constante negative curvature, Bull. Amer. Math. Soc. 77 (1971) 863-877. | MR 284564 | Zbl 0227.53003

[15] Katok A., Nitica V., Torok A., Non-abelian cohomology of abelian Anosov actions, Ergodic Theory Dynamical Systems 20 (2000) 259-288. | MR 1747022 | Zbl 0977.57042

[16] Lawson B., Foliations, Bull. Amer. Math. Soc. 80 (1974) 369-418. | MR 343289 | Zbl 0293.57014

[17] Ledrappier F., Positivity of the exponent for stationary sequences of matrices, in: Lecture Notes in Math., 1186, 1986, pp. 56-73. | MR 850070 | Zbl 0591.60036

[18] Ledrappier F., Royer G., Croissance exponentielle de certains produits aléatoires de matrices, C. Acad. Sci. 280 (1980) 513-514. | MR 571564 | Zbl 0437.60048

[19] Leplaideur R., Local product structure for equilibrium states, Trans. Amer. Math. Soc. 352 (2000) 1889-1912. | MR 1661262 | Zbl 0995.37017

[20] Oseledets V., A multiplicative ergodic theorem, Trans. Moscow Math. Soc. 19 (1968) 197-231. | Zbl 0236.93034

[21] Parry W., Pollicott M., Zeta functions and the periodic orbit structure of hyperbolic systems, Astérisque 187-188 (1990). | MR 1085356 | Zbl 0726.58003

[22] Rokhlin V., Sellected topics from the metric theory of dynamical systems, Amer. Math. Soc. Transl. 49 (1966) 171-240. | Zbl 0185.21802

[23] Royer G., Croissance exponentielle de produits markoviens de matrices aléatoires, Ann. Inst. Henri Poincaré 16 (1980) 49-62. | Numdam | MR 575176 | Zbl 0433.60073

[24] Ruelle D., A measure associated with Axiom A attractors, Amer. J. Math. 98 (1976) 619-654. | MR 415683 | Zbl 0355.58010

[25] Sinai Ya., Gibbs measures in ergodic theory, Russian Math. Surveys 27 (1972) 21-69. | MR 399421 | Zbl 0255.28016