Partial hyperbolicity for symplectic diffeomorphisms

Vanderlei Horita; Ali Tahzibi

Annales de l'I.H.P. Analyse non linéaire (2006)

  • Volume: 23, Issue: 5, page 641-661
  • ISSN: 0294-1449

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Horita, Vanderlei, and Tahzibi, Ali. "Partial hyperbolicity for symplectic diffeomorphisms." Annales de l'I.H.P. Analyse non linéaire 23.5 (2006): 641-661. <http://eudml.org/doc/78705>.

@article{Horita2006,
author = {Horita, Vanderlei, Tahzibi, Ali},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {partial hyperbolicity; dominated splitting; symplectic diffeomorphisms; robust transitivity; stable ergodicity},
language = {eng},
number = {5},
pages = {641-661},
publisher = {Elsevier},
title = {Partial hyperbolicity for symplectic diffeomorphisms},
url = {http://eudml.org/doc/78705},
volume = {23},
year = {2006},
}

TY - JOUR
AU - Horita, Vanderlei
AU - Tahzibi, Ali
TI - Partial hyperbolicity for symplectic diffeomorphisms
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2006
PB - Elsevier
VL - 23
IS - 5
SP - 641
EP - 661
LA - eng
KW - partial hyperbolicity; dominated splitting; symplectic diffeomorphisms; robust transitivity; stable ergodicity
UR - http://eudml.org/doc/78705
ER -

References

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  2. [2] Arnaud M.-C., The generic symplectic C 1 -diffeomorphisms of four-dimensional symplectic manifolds are hyperbolic, partially hyperbolic or have a completely elliptic periodic point, Ergodic Theory Dynam. Systems22 (6) (2002) 1621-1639. Zbl1030.37037MR1944396
  3. [3] J. Bochi, M. Viana, Lyapunov exponents: How frequently are dynamical systems hyperbolic?, Preprint IMPA, 2003. Zbl1147.37315MR2090775
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  5. [5] Bonatti C., Díaz L.J., Pujals E., A C 1 -generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks or sources, Ann. of Math.157 (2) (2003) 355-418. Zbl1049.37011MR2018925
  6. [6] Bonatti C., Viana M., SRB measures for partially hyperbolic systems whose central direction is mostly contracting, Israel J. Math.115 (2000) 157-193. Zbl0996.37033MR1749677
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  9. [9] Díaz L.J., Pujals E., Ures R., Partial hyperbolicity and robust transitivity, Acta Math.183 (1999) 1-43. Zbl0987.37020MR1719547
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  12. [12] Mañé R., Oseledec's theorem from the generic viewpoint, in: Proceedings of the International Congress of Mathematicians, vols. 1, 2, Warsaw, 1983, PWN, Warsaw, 1984, pp. 1269-1276. Zbl0584.58007MR804776
  13. [13] Newhouse S., Quasi-elliptic periodic points in conservative dynamical systems, Amer. J. Math.99 (5) (1976) 1061-1087. Zbl0379.58011MR455049
  14. [14] Shub M., Topologically transitive diffeomorphisms on T 4 , in: Lecture Notes in Math., vol. 206, Springer-Verlag, 1971, pp. 39. 
  15. [15] Tahzibi A., Stably ergodic systems which are not partially hyperbolic, Israel J. Math.24 (204) (2004) 315-342. Zbl1052.37019MR2085722
  16. [16] Vivier T., Flots robustament transitif sur des variété compactes, C. R. Math. Acad. Sci. Paris337 (12) (2003) 791-796. Zbl1079.37013MR2033121
  17. [17] Xia Z., Homoclinic points in symplectic and volume-preserving diffeomorphisms, Comm. Math. Phys.177 (2) (1996) 435-449. Zbl0959.37050MR1384143
  18. [18] Zehnder E., A note on smoothing symplectic and volume preserving diffeomorphisms, in: Lecture Notes in Math., vol. 597, Springer-Verlag, 1977, pp. 828-854. Zbl0363.58004MR467846

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