Partial hyperbolicity for symplectic diffeomorphisms
Annales de l'I.H.P. Analyse non linéaire, Volume 23 (2006) no. 5, p. 641-661
@article{AIHPC_2006__23_5_641_0,
     author = {Horita, Vanderlei and Tahzibi, Ali},
     title = {Partial hyperbolicity for symplectic diffeomorphisms},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {23},
     number = {5},
     year = {2006},
     pages = {641-661},
     doi = {10.1016/j.anihpc.2005.06.002},
     zbl = {05072655},
     mrnumber = {2259610},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2006__23_5_641_0}
}
Horita, Vanderlei; Tahzibi, Ali. Partial hyperbolicity for symplectic diffeomorphisms. Annales de l'I.H.P. Analyse non linéaire, Volume 23 (2006) no. 5, pp. 641-661. doi : 10.1016/j.anihpc.2005.06.002. http://www.numdam.org/item/AIHPC_2006__23_5_641_0/

[1] A. Arbieto, C. Matheus, A pasting lemma I: the case of vector fields, Preprint, IMPA, 2003.

[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. Systems 22 (6) (2002) 1621-1639. | MR 1944396 | Zbl 1030.37037

[3] J. Bochi, M. Viana, Lyapunov exponents: How frequently are dynamical systems hyperbolic?, Preprint IMPA, 2003. | MR 2090775

[4] Bonatti C., Díaz L.J., Nonhyperbolic transitive diffeomorphisms, Ann. of Math. 143 (1996) 357-396. | MR 1381990 | Zbl 0852.58066

[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. | MR 2018925 | Zbl 1049.37011

[6] Bonatti C., Viana M., SRB measures for partially hyperbolic systems whose central direction is mostly contracting, Israel J. Math. 115 (2000) 157-193. | MR 1749677 | Zbl 0996.37033

[7] Burns K., Pugh C., Shub M., Wilkinson A., Recent results about stable ergodicity, Proc. Sympos. Amer. Math. Soc. 69 (2001) 327-366. | MR 1858538 | Zbl 1012.37019

[8] Dacorogna B., Moser J., On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1) (1990) 1-26. | Numdam | MR 1046081 | Zbl 0707.35041

[9] Díaz L.J., Pujals E., Ures R., Partial hyperbolicity and robust transitivity, Acta Math. 183 (1999) 1-43. | MR 1719547 | Zbl 0987.37020

[10] Mañé R., Contributions to the stability conjecture, Topology 17 (1978) 383-396. | MR 516217 | Zbl 0405.58035

[11] Mañé R., An ergodic closing lemma, Ann. of Math. 116 (1982) 503-540. | MR 678479 | Zbl 0511.58029

[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. | MR 804776 | Zbl 0584.58007

[13] Newhouse S., Quasi-elliptic periodic points in conservative dynamical systems, Amer. J. Math. 99 (5) (1976) 1061-1087. | MR 455049 | Zbl 0379.58011

[14] Shub M., Topologically transitive diffeomorphisms on T 4 , in: Lecture Notes in Math., vol. 206, Springer-Verlag, 1971, pp. 39.

[15] Tahzibi A., Stably ergodic systems which are not partially hyperbolic, Israel J. Math. 24 (204) (2004) 315-342. | MR 2085722 | Zbl 1052.37019

[16] Vivier T., Flots robustament transitif sur des variété compactes, C. R. Math. Acad. Sci. Paris 337 (12) (2003) 791-796. | MR 2033121 | Zbl 1079.37013

[17] Xia Z., Homoclinic points in symplectic and volume-preserving diffeomorphisms, Comm. Math. Phys. 177 (2) (1996) 435-449. | MR 1384143 | Zbl 0959.37050

[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. | MR 467846 | Zbl 0363.58004