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On the approximation of Hénon-like attractors by homoclinic tangencies

Published online by Cambridge University Press:  14 October 2010

Raúl Ures
Raúl Ures
Affiliation:
IMERL, Facultad de Ingenieía, CC30 Montevideo, Uruguay
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Abstract

We prove that the diffeomorphisms with strange attractors shown to exist elsewhere are approximated by diffeomorphisms exhibiting homoclinic tangencies. As a consequence for the Hénon family these diffeomorphisms are approximated by diffeomorphisms exhibiting periodic attractors. This answers a question posed by Benedicks and Carleson.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 6 , December 1995 , pp. 1223 - 1229
Copyright
Copyright © Cambridge University Press 1995

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References

REFERENCES

[BC]Benedicks, M. and Carleson, L.. The dynamics of the Hénon map. Ann. Math. 133 (1991), 73–169.CrossRefGoogle Scholar
[MV]Mora, L. and Viana, M.. The abundance of strange attractors, Acta Math. 171 (1993), 1–71.CrossRefGoogle Scholar
[Nl]Newhouse, S.. The abundance of wild hyperbolic sets and non smooth stable sets for diffeomorphisms. Publ. IHES 50 (1979), 101–151.CrossRefGoogle Scholar
[PT1]Palis, J. and Takensa, F.. Hyperbolicity and Sensitive-chaotic Dynamics at Homoclinic Bifurcations, Fractal Dimensions and Infinitely Many Attractors. Cambridge University Press: Cambridge, 1993.Google Scholar
[PT2]Palis, J. and Takens, F.. Hyperbolicity and the creation of homoclinic orbits. Ann. Math. 125 (1987), 337–374.CrossRefGoogle Scholar
[PY]Palis, J. and Yoccoz, J. C.. Homoclinic bifurcations: Large Haussdorf dimension and non-hyperbolic behaviour. Ada Math. (To appear).Google Scholar
[R]Robinson, C.. Bifurcation to infinitely many sinks. Commun. Math. Phys. 90 (1983), 433–459.CrossRefGoogle Scholar
[T]Takens, F.. Abundance of generic homoclinic tangencies in real analytic families of diffeomorphisms. Bol. Soc. Bras. Mat. 22 (1992), 191–214.CrossRefGoogle Scholar
[V]Viana, M.. Strange attractors in higher dimensions. Bol. Soc. Bras. Mat. 24 (1993), 13–62.CrossRefGoogle Scholar
[YA]Yorke, J. and Alligood, K.. Cascades of period-doubling bifurcations: a prerequisite for horseshoes. Bull. Am. Math. Soc. (New Series) 9 (1983), 319–322.CrossRefGoogle Scholar