Approximation des ensembles ω-limites des difféomorphismes par des orbites périodiques

Marie-Claude Arnaud

Annales scientifiques de l'École Normale Supérieure (2003)

  • Volume: 36, Issue: 2, page 173-190
  • ISSN: 0012-9593

How to cite


Arnaud, Marie-Claude. "Approximation des ensembles ω-limites des difféomorphismes par des orbites périodiques." Annales scientifiques de l'École Normale Supérieure 36.2 (2003): 173-190. <>.

author = {Arnaud, Marie-Claude},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {-limit sets; diffeomorphisms; periodic orbits; attractors},
language = {fre},
number = {2},
pages = {173-190},
publisher = {Elsevier},
title = {Approximation des ensembles ω-limites des difféomorphismes par des orbites périodiques},
url = {},
volume = {36},
year = {2003},

AU - Arnaud, Marie-Claude
TI - Approximation des ensembles ω-limites des difféomorphismes par des orbites périodiques
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2003
PB - Elsevier
VL - 36
IS - 2
SP - 173
EP - 190
LA - fre
KW - -limit sets; diffeomorphisms; periodic orbits; attractors
UR -
ER -


  1. [1] Arnaud M.-C., Le “closing lemma” en topologie C1, Mem. Soc. Math. Fr, Nouv. Série74 (1998). Zbl0920.58039
  2. [2] Arnaud M.-C., Un lemme de fermeture d'orbites : le “orbit closing lemma”, C.R.A.S., Ser. I323 (1996) 1175-1178. Zbl0867.58040
  3. [3] Arnaud M.-C., Création de connexions en topologie C1, Ergodic Theory Dynam. Systems21 (2001) 1-43. Zbl0997.37007MR1827109
  4. [4] Arnaud M.-C., The generic symplectic C1-diffeomorphisms of 4-dimensional symplectic manifolds are hyperbolic, partially hyperbolic or have a completely periodic point, Ergodic Theory Dynam. Systems, à paraître. Zbl1030.37037
  5. [5] Arnaud M.-C., Création de points périodiques de tous types au voisinage des tores K.A.M, Bull. Soc. Math. France123 (1995) 591-603. Zbl0853.58046MR1373949
  6. [6] Bonatti C., Diaz L., Pujals E., A C1-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks or sources, preprint. Zbl1049.37011MR2018925
  7. [7] Bonatti C., Diaz L., Connexions hétéroclines et généricité d'une infinité de puits et de sources, Ann. Sci. Ecole Norm. Sup.32 (1999) 135-150. Zbl0944.37012MR1670524
  8. [8] Brin M.I., Pesin S.A., Partially hyperbolic dynamical systems, Math. USSR Izvestija8 (1974) 177-218. Zbl0309.58017
  9. [9] Hayashi S., Connecting invariant manifolds and the solution of the C1-stability and Ω-stability conjectures for flows, Ann. Math.145 (1997) 81-137. Zbl0871.58067
  10. [10] Hayashi S., Hyperbolicity, stability and the creation of homoclinic points, Documenta Mathematica, Extra Vol. ICMII (1998) 789-796. Zbl0911.58023MR1648126
  11. [11] Kuratowski C., Gabay J. (Ed.), Topologie, 1992. Zbl0849.01044MR1296876
  12. [12] Mañé R., An ergodic closing lemma, Ann. Math.116 (1982) 503-540. Zbl0511.58029MR678479
  13. [13] Morales C.A., Pacifico M.-J., Lyapunov stability of generic ω-limit sets, preprint. Zbl1162.37302
  14. [14] Newhouse S., Diffeomorphisms with infinitely many sinks, Topology12 (1974) 9-18. Zbl0275.58016MR339291
  15. [15] Newhouse S., Quasi-elliptic points in conservative dynamical systems, Amer. J. Math.99 (1977) 1081-1087. Zbl0379.58011MR455049
  16. [16] Pugh C., Robinson C., The C1 closing lemma, including Hamiltonians, Ergodic Theory Dynam. Systems3 (1983) 261-314. Zbl0548.58012MR742228
  17. [17] Shub M., Stabilité globale des systèmes dynamiques, Astérisque56 (1978). Zbl0396.58014MR513592
  18. [18] Xia Z., Homoclinic points in symplectic and volume preserving diffeomorphisms, Comm. Math. Phys.117 (1996) 435-449. Zbl0959.37050MR1384143

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