Plenty of elliptic islands for the standard family of area preserving maps
Duarte, Pedro
Annales de l'I.H.P. Analyse non linéaire, Tome 11 (1994), p. 359-409 / Harvested from Numdam
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Publié le : 1994-01-01
@article{AIHPC_1994__11_4_359_0,
     author = {Duarte, Pedro},
     title = {Plenty of elliptic islands for the standard family of area preserving maps},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {11},
     year = {1994},
     pages = {359-409},
     mrnumber = {1287238},
     zbl = {0838.58030},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1994__11_4_359_0}
}

Duarte, Pedro. Plenty of elliptic islands for the standard family of area preserving maps. Annales de l'I.H.P. Analyse non linéaire, Tome 11 (1994) pp. 359-409. http://gdmltest.u-ga.fr/item/AIHPC_1994__11_4_359_0/

[A] V. Arnold, Methods Mathematiques de la Mécanique Classique, Editions MIR, 1976. | MR 474391 | Zbl 0385.70001

[C1] L. Carleson, The dynamics of non uniform hyperbolic systems in two variables, Proceedings of the International Congress of Mathematicians, Kyoto, Japan, 1990. | MR 1159309 | Zbl 0751.58026

[C2] L. Carleson, Stochastic Models of some Dynamical Systems, Lecture Notes in Mathematics, 1469, 1991, pp. 1-12. | MR 1122610 | Zbl 0777.58023

[G] D. Goroff Hyperbolic sets for twist maps, Ergodic Theory and Dynamical Systems, 5, 1985, pp. 337-339. | MR 805834 | Zbl 0551.58028

[HP] M. Hirsch and C. Pugh, Stable Manifolds and Hyperbolic sets, Global Analysis, Proc. Symp. in Pure Math., Vol XIV, Amer. Math. Soc., 1970. | MR 271991 | Zbl 0215.53001

[HPS] M. Hirsch, C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics, 583, 1977. | MR 501173 | Zbl 0355.58009

[MR] L. Mora and N. Romero, Elliptic orbits in homoclinic bifurcations, Preprint, 1993.

[Mo] J. Moser, Stable and Random Motions in Dynamical Systems, with special emphasis to Celestial Mechanics, Princeton Univ. Press, 1973. | MR 442980 | Zbl 0271.70009

[N1] S. Newhouse, Quasi-elliptic periodic points in conservative dynamical systems, American Journal of Mathematics, Vol 99, No 5, 1977, pp. 1061-1067. | MR 455049 | Zbl 0379.58011

[N2] S. Newhouse, Non density of Axiom A(a) on S2 , Proceedings of AMS Symp. Pure Math., 14, 1970, pp. 191-202. | MR 277005 | Zbl 0206.25801

[N3] S. Newhouse, Diffeomorphisms with infinitely many sinks, Topology, 13, 1974, pp 9-18. | MR 339291 | Zbl 0275.58016

[N4] S. Newhouse, The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Publ. Math. IHES, 50, 1979, pp. 101-151. | Numdam | MR 556584 | Zbl 0445.58022

[NPT] S. Newhouse, J. Palis and F. Takens, Bifurcations and Stability of families of diffeomorphisms, Publ. Math. IHES, 57, 1983, pp. 5-71. | Numdam | MR 699057 | Zbl 0518.58031

[PT] J. Palis and F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge studies in advanced mathematics, 35, 1993. | MR 1237641 | Zbl 0790.58014

[Ro] N. Romero, Persistence of homoclinic tangencies in higher dimensions, Preprint, 1992. | MR 1346398

[S] M. Shub, Global Stability of Dynamical Systems, Springer Verlag, 1978. | MR 513592 | Zbl 0606.58003

[VT] P. Veerman and F. Tangerman, Intersection properties of invariant manifolds in certain twist maps, Commun. Math. Phys., 139, 1991, pp. 245-265. | MR 1120139 | Zbl 0745.58039