Infinitely many coexisting strange attractors

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 15, Issue 5, 1998, Pages 539-579

  Colli, Eduardo ^a  

^a IMPA   (Brazil)

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[No Author keywords available]

Indexed keywords

EID: 0000709901     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(98)80001-2     Document Type: Article

References (18)

1. M. BENEDICKS and L. CARLESON, The dynamics of the Hénon map, Ann. Math., Vol. 133, 1991, pp. 73-169.
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.
4. R. KRAFT, Intersection of thick Cantor sets, Mem. Amer. Math. Soc., Vol. 97, No. 468(2), 1992, pp. 1-119.
5. 2, Proc. A.M.S. Symp. Pure Math., Vol. 14, 1970, pp. 191-202.
6. S. NEWHOUSE, Diffeomorphisms with infinitely many sinks, Topology, Vol. 13, 1974, pp. 9-18.
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.
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.
9. L. MORA and M. VIANA, Abundance of strange attractors, Acta Math., Vol. 171, 1993, pp. 1-71.
10. H. POINCARÉ, Sur le problème des trois corps et les équations de la dynamique (Mémoire couronné du prise de S.M. le roi Oscar II de Suède), Acta Math., Vol. 13, 1890, pp. 1 -270.
11. A. PUMARIÑO and J. A. RODRIGUEZ, Coexistence and persistence of strange attractors, 1994, to appear.
12. J. PALIS and F. TAKENS. Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge University Press, 1993.
13. C. ROBINSON, Bifurcation to infinitely many sinks, Comm. Math. Phys., Vol. 90, 1983, pp. 433-459.
14. S. STERNBERG, Local contractions and a theorem of Poincaré, Amer. J. Math., Vol. 79, 1957, pp. 809-824.
15. S. STERNBERG, On the structure of local homeomorphisms of Euclidean n-space, II, Amer. J. Math., Vol. 80, 1958, pp. 623-631.
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.
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.