Infinitely many coexisting strange attractors

Eduardo Colli

Annales de l'I.H.P. Analyse non linéaire (1998)

  • Volume: 15, Issue: 5, page 539-579
  • ISSN: 0294-1449

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Colli, Eduardo. "Infinitely many coexisting strange attractors." Annales de l'I.H.P. Analyse non linéaire 15.5 (1998): 539-579. <http://eudml.org/doc/78448>.

@article{Colli1998,
author = {Colli, Eduardo},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {homoclinic tangency; unfoldings; Hénon-like strange attractor; heteroclinic tangency; perturbation},
language = {eng},
number = {5},
pages = {539-579},
publisher = {Gauthier-Villars},
title = {Infinitely many coexisting strange attractors},
url = {http://eudml.org/doc/78448},
volume = {15},
year = {1998},
}

TY - JOUR
AU - Colli, Eduardo
TI - Infinitely many coexisting strange attractors
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1998
PB - Gauthier-Villars
VL - 15
IS - 5
SP - 539
EP - 579
LA - eng
KW - homoclinic tangency; unfoldings; Hénon-like strange attractor; heteroclinic tangency; perturbation
UR - http://eudml.org/doc/78448
ER -

References

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  1. [1] M. Benedicks and L. Carleson, The dynamics of the Hénon map, Ann. Math., Vol. 133, 1991, pp. 73-169. Zbl0724.58042MR1087346
  2. [2] E. Catsigeras, Cascades of period doubling of stable codimension one, Thesis IMPA, 1995. 
  3. [3] J.-M. Gambaudo and C. Tresser, Diffeomorphisms with infinitely many strange attractors, J. of Complexity, Vol. 6, 1990, pp. 409-416. Zbl0717.58041MR1085387
  4. [4] R. Kraft, Intersection of thick Cantor sets, Mem. Amer. Math. Soc., Vol. 97, No. 468(2), 1992, pp. 1-119. Zbl0753.28009MR1106988
  5. [5] S. Newhouse, Non-density of Axiom A(a) on S2, Proc. A.M.S. Symp. Pure Math., Vol. 14, 1970, pp. 191-202. Zbl0206.25801MR277005
  6. [6] S. Newhouse, Diffeomorphisms with infinitely many sinks, Topology, Vol. 13, 1974, pp. 9-18. Zbl0275.58016MR339291
  7. [7] S. Newhouse, The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Publ. Math. I.H.E.S., Vol. 50, 1979, pp. 101-151. Zbl0445.58022MR556584
  8. [8] S. Newhouse, J. Palis and F. Takens, Bifurcations and stability of families of diffeomorphisms, Publ. Math. I.H.E.S., Vol. 57, 1983, pp. 5-71. Zbl0518.58031MR699057
  9. [9] L. Mora and M. Viana, Abundance of strange attractors, Acta Math., Vol. 171, 1993, pp. 1-71. Zbl0815.58016MR1237897
  10. [10] H. Poincaré, Sur le problème des trois corps et les equations de la dynamique (Mémoire couronné du prise de S.M. le roi Oscar II de Suède), Acta Math., Vol. 13, 1890, pp. 1-270. JFM22.0907.01
  11. [11] A. PUMARIÑO and J.A. Rodriguez, Coexistence and persistence of strange attractors, 1994, to appear. Zbl0877.58041MR1456717
  12. [12] J. Palis and F. Takens. Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge University Press, 1993. Zbl0790.58014MR1237641
  13. [13] C. Robinson, Bifurcation to infinitely many sinks, Comm. Math. Phys., Vol. 90, 1983, pp. 433-459. Zbl0531.58035MR719300
  14. [14] S. Sternberg, Local contractions and a theorem of Poincaré, Amer. J. Math., Vol. 79, 1957, pp. 809-824. Zbl0080.29902MR96853
  15. [15] S. Sternberg, On the structure of local homeomorphisms of Euclidean n-space, II, Amer. J. Math., Vol. 80, 1958, pp. 623-631. Zbl0083.31406MR96854
  16. [16] R. Ures, Approximating a Hénon-like strange attractor by a homoclinic tangency and an attracting cycle, to appear in Erg. Th. and Dyn. Syst. 
  17. [17] M. Viana, Strange attractors in higher dimensions, Bol. Soc. Bras. Mat., Vol. 24(1), 1993, pp. 13-62. Zbl0784.58044MR1224299
  18. [18] J.A. Yorke and K.T. Alligood, Cascades of period doubling bifurcations: a pre-requisite for horseshoes, Bull. A.M.S., Vol. 9, 1983, pp. 319-322. Zbl0541.58039MR714994

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