Uniform (projective) hyperbolicity or no hyperbolicity : a dichotomy for generic conservative maps

Jairo Bochi; Marcelo Viana

Annales de l'I.H.P. Analyse non linéaire (2002)

  • Volume: 19, Issue: 1, page 113-123
  • ISSN: 0294-1449

How to cite

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Bochi, Jairo, and Viana, Marcelo. "Uniform (projective) hyperbolicity or no hyperbolicity : a dichotomy for generic conservative maps." Annales de l'I.H.P. Analyse non linéaire 19.1 (2002): 113-123. <http://eudml.org/doc/78536>.

@article{Bochi2002,
author = {Bochi, Jairo, Viana, Marcelo},
journal = {Annales de l'I.H.P. Analyse non linéaire},
language = {eng},
number = {1},
pages = {113-123},
publisher = {Elsevier},
title = {Uniform (projective) hyperbolicity or no hyperbolicity : a dichotomy for generic conservative maps},
url = {http://eudml.org/doc/78536},
volume = {19},
year = {2002},
}

TY - JOUR
AU - Bochi, Jairo
AU - Viana, Marcelo
TI - Uniform (projective) hyperbolicity or no hyperbolicity : a dichotomy for generic conservative maps
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2002
PB - Elsevier
VL - 19
IS - 1
SP - 113
EP - 123
LA - eng
UR - http://eudml.org/doc/78536
ER -

References

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  1. [1] Arnaud M.-C., The generic symplectic C1 diffeomorphisms of 4-dimensional symplectic manifolds are hyperbolic, partially hyperbolic, or have a completely elliptic point, preprint Orsay, 2000. MR1809443
  2. [2] Avila A., Bochi J., A formula with some applications to the theory of Lyapunov exponents, www.preprint.impa.br. Zbl1022.37019
  3. [3] Bochi J., Genericity of zero Lyapunov exponents, www.preprint.impa.br. Zbl1023.37006MR1944399
  4. [4] Bochi J., Viana M., A sharp dichotomy for conservative systems: zero Lyapunov exponents or projective hyperbolicity, in preparation. Zbl1125.37308
  5. [5] Bonatti C., Viana M., Lyapunov exponents with multiplicity 1 for deterministic products of matrices, www.preprint.impa.br. Zbl1087.37017MR2104587
  6. [6] Bowen R., Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lect. Notes in Math., 470, Springer Verlag, 1975. Zbl0308.28010MR442989
  7. [7] Herman M., Une méthode pour minorer les exposants de Lyapounov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2, Comment. Math. Helvetici58 (1983) 453-502. Zbl0554.58034MR727713
  8. [8] Ledrappier F., Quelques propriétés des exposants caractéristiques, École d'Été de Probabilités de Saint-Flour XII, 1982, Lect. Notes in Math., 1097, Springer Verlag, 1984. Zbl0578.60029MR876081
  9. [9] Mañé R., Oseledec's theorem from the generic viewpoint, in: Procs. Intern. Congress Math. Warszawa Vol. 2, 1983, pp. 1259-1276. Zbl0584.58007
  10. [10] Mañé R., The Lyapunov exponents of generic area preserving diffeomorphisms, in: Procs. Intern. Conf. Dynam. Syst., Montevideo, Pitman RNMS, 362, 1996, pp. 110-119. Zbl0870.58083MR1460799
  11. [11] Oseledets V., A multiplicative ergodic theorem, Trudy Moscow Math. Obs.19 (1968) 179-210. Zbl0236.93034MR240280
  12. [12] Ruelle D., Analyticity properties of the characteristic exponents of random matrix products, Adv. Math.32 (1979) 68-80. Zbl0426.58018MR534172

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