Plenty of elliptic islands for the standard family of area preserving maps

Pedro Duarte

Annales de l'I.H.P. Analyse non linéaire (1994)

  • Volume: 11, Issue: 4, page 359-409
  • ISSN: 0294-1449

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Duarte, Pedro. "Plenty of elliptic islands for the standard family of area preserving maps." Annales de l'I.H.P. Analyse non linéaire 11.4 (1994): 359-409. <http://eudml.org/doc/78337>.

@article{Duarte1994,
author = {Duarte, Pedro},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {unfolding of a homoclinic tangency; thickness of a hyperbolic basic set},
language = {eng},
number = {4},
pages = {359-409},
publisher = {Gauthier-Villars},
title = {Plenty of elliptic islands for the standard family of area preserving maps},
url = {http://eudml.org/doc/78337},
volume = {11},
year = {1994},
}

TY - JOUR
AU - Duarte, Pedro
TI - Plenty of elliptic islands for the standard family of area preserving maps
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1994
PB - Gauthier-Villars
VL - 11
IS - 4
SP - 359
EP - 409
LA - eng
KW - unfolding of a homoclinic tangency; thickness of a hyperbolic basic set
UR - http://eudml.org/doc/78337
ER -

References

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  1. [A] V. Arnold, Methods Mathematiques de la Mécanique Classique, Editions MIR, 1976. Zbl0385.70001MR474391
  2. [C1] L. Carleson, The dynamics of non uniform hyperbolic systems in two variables, Proceedings of the International Congress of Mathematicians, Kyoto, Japan, 1990. Zbl0751.58026MR1159309
  3. [C2] L. Carleson, Stochastic Models of some Dynamical Systems, Lecture Notes in Mathematics, 1469, 1991, pp. 1-12. Zbl0777.58023MR1122610
  4. [G] D. GoroffHyperbolic sets for twist maps, Ergodic Theory and Dynamical Systems, 5, 1985, pp. 337-339. Zbl0551.58028MR805834
  5. [HP] M. Hirsch and C. Pugh, Stable Manifolds and Hyperbolic sets, Global Analysis, Proc. Symp. in Pure Math., Vol XIV, Amer. Math. Soc., 1970. Zbl0215.53001MR271991
  6. [HPS] M. Hirsch, C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics, 583, 1977. Zbl0355.58009MR501173
  7. [MR] L. Mora and N. Romero, Elliptic orbits in homoclinic bifurcations, Preprint, 1993. 
  8. [Mo] J. Moser, Stable and Random Motions in Dynamical Systems, with special emphasis to Celestial Mechanics, Princeton Univ. Press, 1973. Zbl0271.70009MR442980
  9. [N1] S. Newhouse, Quasi-elliptic periodic points in conservative dynamical systems, American Journal of Mathematics, Vol 99, No 5, 1977, pp. 1061-1067. Zbl0379.58011MR455049
  10. [N2] S. Newhouse, Non density of Axiom A(a) on S2 , Proceedings of AMS Symp. Pure Math., 14, 1970, pp. 191-202. Zbl0206.25801MR277005
  11. [N3] S. Newhouse, Diffeomorphisms with infinitely many sinks, Topology, 13, 1974, pp 9-18. Zbl0275.58016MR339291
  12. [N4] S. Newhouse, The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Publ. Math. IHES, 50, 1979, pp. 101-151. Zbl0445.58022MR556584
  13. [NPT] S. Newhouse, J. Palis and F. Takens, Bifurcations and Stability of families of diffeomorphisms, Publ. Math. IHES, 57, 1983, pp. 5-71. Zbl0518.58031MR699057
  14. [PT] J. Palis and F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge studies in advanced mathematics, 35, 1993. Zbl0790.58014MR1237641
  15. [Ro] N. Romero, Persistence of homoclinic tangencies in higher dimensions, Preprint, 1992. MR1346398
  16. [S] M. Shub, Global Stability of Dynamical Systems, Springer Verlag, 1978. Zbl0606.58003MR513592
  17. [VT] P. Veerman and F. Tangerman, Intersection properties of invariant manifolds in certain twist maps, Commun. Math. Phys., 139, 1991, pp. 245-265. Zbl0745.58039MR1120139

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