Infinitely many coexisting strange attractors
Colli, Eduardo
Annales de l'I.H.P. Analyse non linéaire, Tome 15 (1998), p. 539-579 / Harvested from Numdam
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@article{AIHPC_1998__15_5_539_0,
     author = {Colli, Eduardo},
     title = {Infinitely many coexisting strange attractors},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {15},
     year = {1998},
     pages = {539-579},
     mrnumber = {1643393},
     zbl = {0932.37015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1998__15_5_539_0}
}

Colli, Eduardo. Infinitely many coexisting strange attractors. Annales de l'I.H.P. Analyse non linéaire, Tome 15 (1998) pp. 539-579. http://gdmltest.u-ga.fr/item/AIHPC_1998__15_5_539_0/

[1] M. Benedicks and L. Carleson, The dynamics of the Hénon map, Ann. Math., Vol. 133, 1991, pp. 73-169. | MR 1087346 | Zbl 0724.58042

[2] E. Catsigeras, Cascades of period doubling of stable codimension one, Thesis IMPA, 1995.

[3] J.-M. Gambaudo and C. Tresser, Diffeomorphisms with infinitely many strange attractors, J. of Complexity, Vol. 6, 1990, pp. 409-416. | MR 1085387 | Zbl 0717.58041

[4] R. Kraft, Intersection of thick Cantor sets, Mem. Amer. Math. Soc., Vol. 97, No. 468(2), 1992, pp. 1-119. | MR 1106988 | Zbl 0753.28009

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

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

[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. | Numdam | MR 556584 | Zbl 0445.58022

[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. | Numdam | MR 699057 | Zbl 0518.58031

[9] L. Mora and M. Viana, Abundance of strange attractors, Acta Math., Vol. 171, 1993, pp. 1-71. | MR 1237897 | Zbl 0815.58016

[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. | JFM 22.0907.01

[11] A. Pumariño and J.A. Rodriguez, Coexistence and persistence of strange attractors, 1994, to appear. | MR 1456717 | Zbl 0877.58041

[12] J. Palis and F. Takens. Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge University Press, 1993. | MR 1237641 | Zbl 0790.58014

[13] C. Robinson, Bifurcation to infinitely many sinks, Comm. Math. Phys., Vol. 90, 1983, pp. 433-459. | MR 719300 | Zbl 0531.58035

[14] S. Sternberg, Local contractions and a theorem of Poincaré, Amer. J. Math., Vol. 79, 1957, pp. 809-824. | MR 96853 | Zbl 0080.29902

[15] S. Sternberg, On the structure of local homeomorphisms of Euclidean n-space, II, Amer. J. Math., Vol. 80, 1958, pp. 623-631. | MR 96854 | Zbl 0083.31406

[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] M. Viana, Strange attractors in higher dimensions, Bol. Soc. Bras. Mat., Vol. 24(1), 1993, pp. 13-62. | MR 1224299 | Zbl 0784.58044

[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. | MR 714994 | Zbl 0541.58039