Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices

Christian Bonatti; Xavier Gómez-Mont; Marcelo Viana

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 4, page 579-624
  • ISSN: 0294-1449

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Bonatti, Christian, Gómez-Mont, Xavier, and Viana, Marcelo. "Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices." Annales de l'I.H.P. Analyse non linéaire 20.4 (2003): 579-624. <http://eudml.org/doc/78590>.

@article{Bonatti2003,
author = {Bonatti, Christian, Gómez-Mont, Xavier, Viana, Marcelo},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Linear cocycle; Lyapunov exponents; vector bundle; projective bundle; holomorphic; foliation; group representations},
language = {fre},
number = {4},
pages = {579-624},
publisher = {Elsevier},
title = {Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices},
url = {http://eudml.org/doc/78590},
volume = {20},
year = {2003},
}

TY - JOUR
AU - Bonatti, Christian
AU - Gómez-Mont, Xavier
AU - Viana, Marcelo
TI - Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 4
SP - 579
EP - 624
LA - fre
KW - Linear cocycle; Lyapunov exponents; vector bundle; projective bundle; holomorphic; foliation; group representations
UR - http://eudml.org/doc/78590
ER -

References

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  1. [1] Anosov D., Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Inst. Math.90 (1967). Zbl0176.19101MR224110
  2. [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. Zbl0967.37020MR1699356
  3. [3] J. Bochi, Genericity of zero Lyapunov exponents, Ergodic Theory Dynamical Systems 22 (2002). Zbl1023.37006MR1944399
  4. [4] C. Bonatti, X. Gómez-Mont, R. Vila, The foliated geodesic flow of Ricatti equations, Pre-publication Dijon. 
  5. [5] C. Bonatti, X. Gómez-Mont, Sur le comportement statistique des feuilles de certains feuilletages holomorphes, Enseignement Mathématique 38 (2001). Zbl1010.37025MR1929320
  6. [6] Bowen R., Symbolic dynamics for hyperbolic flows, Amer. J. Math.95 (1973) 428-459. Zbl0282.58009MR339281
  7. [7] Bowen R., Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lect. Notes in Math., 470, Springer-Verlag, 1975. Zbl0308.28010MR442989
  8. [8] Bowen R., Ruelle D., The ergodic theory of Axiom A flows, Invent. Math.29 (1975) 181-202. Zbl0311.58010MR380889
  9. [9] Brin Ya., Pesin Ya., Partially hyperbolic systems, Akad. Nauk SSSR1 (1974) 170-212. Zbl0304.58017
  10. [10] Furstenberg H., Noncommuting random products, Trans. Amer. Math. Soc.108 (1963) 377-428. Zbl0203.19102MR163345
  11. [11] Guivarc'h Y., Raugi A., Products of random matrices : convergence theorems, Contemp. Math.50 (1986) 31-54. Zbl0592.60015MR841080
  12. [12] Haydn N., Canonical product structure of equlibrium states, Rand. Comput. Dynam.2 (1994) 79-96. Zbl0810.58030MR1265227
  13. [13] Hirsch M., Pugh C., Shub M., Invariant Manifolds, Lect. Notes in Math., 583, Springer-Verlag, 1977. Zbl0355.58009MR501173
  14. [14] Hopf E., Ergodic theory and the geodesic flow on surfaces on constante negative curvature, Bull. Amer. Math. Soc.77 (1971) 863-877. Zbl0227.53003MR284564
  15. [15] Katok A., Nitica V., Torok A., Non-abelian cohomology of abelian Anosov actions, Ergodic Theory Dynamical Systems20 (2000) 259-288. Zbl0977.57042MR1747022
  16. [16] Lawson B., Foliations, Bull. Amer. Math. Soc.80 (1974) 369-418. Zbl0293.57014MR343289
  17. [17] Ledrappier F., Positivity of the exponent for stationary sequences of matrices, in: Lecture Notes in Math., 1186, 1986, pp. 56-73. Zbl0591.60036MR850070
  18. [18] Ledrappier F., Royer G., Croissance exponentielle de certains produits aléatoires de matrices, C. Acad. Sci.280 (1980) 513-514. Zbl0437.60048MR571564
  19. [19] Leplaideur R., Local product structure for equilibrium states, Trans. Amer. Math. Soc.352 (2000) 1889-1912. Zbl0995.37017MR1661262
  20. [20] Oseledets V., A multiplicative ergodic theorem, Trans. Moscow Math. Soc.19 (1968) 197-231. Zbl0236.93034
  21. [21] Parry W., Pollicott M., Zeta functions and the periodic orbit structure of hyperbolic systems, Astérisque187–188 (1990). Zbl0726.58003MR1085356
  22. [22] Rokhlin V., Sellected topics from the metric theory of dynamical systems, Amer. Math. Soc. Transl.49 (1966) 171-240. Zbl0185.21802
  23. [23] Royer G., Croissance exponentielle de produits markoviens de matrices aléatoires, Ann. Inst. Henri Poincaré16 (1980) 49-62. Zbl0433.60073MR575176
  24. [24] Ruelle D., A measure associated with Axiom A attractors, Amer. J. Math.98 (1976) 619-654. Zbl0355.58010MR415683
  25. [25] Sinai Ya., Gibbs measures in ergodic theory, Russian Math. Surveys27 (1972) 21-69. Zbl0255.28016MR399421

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