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The transversal homoclinic points are dense in the codimension-1 Hénon-like strange attractors
Author(s):
Yongluo
Cao
Journal:
Proc. Amer. Math. Soc.
127
(1999),
1877-1883.
MSC (1991):
Primary 58F11, 58F12
Posted:
February 18, 1999
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Abstract:
We consider the codimension-1 Hénon-like strange attractors . We prove that the transversal homoclinic points are dense in , and that hyperbolic periodic points are dense in . Moreover the hyperbolic periodic points that are heteroclinically related to the primary fixed point ( transversal intersection of stable and unstable manifolds) are dense in .
References:
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- 2.
- M.Benedicks & L.S.Young, Sinai-Bowen-Ruelle measures for certain Hénon maps, Inventions Math. 112 (1993), 541-576. MR 94e:58074
- 3.
- M.Hénon, A two-dimensional mapping with a strange attractor, Commun. Math. Phys 50 (1976), 69-77. MR 54:10917
- 4.
- L.Mora & M.Viana, Abundance of strange attractors, Acta .Math. 171 (1993), 1-71. MR 94k:58089
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- J.Palis & F.Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge Press, 1993. MR 94h:58129
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- M.Viana, Strange attractors in higher dimensions, Bull.Braz.Math.Soc. 24 (1993), 13-62. MR 94k:58093
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Additional Information:
Yongluo
Cao
Affiliation:
Department of Mathematics, Suzhou University, Suzhou 215006, Jiangsu, People's Republic of China
Email:
ylcao@nsad.suda.edu.cn
DOI:
10.1090/S0002-9939-99-04787-5
PII:
S 0002-9939(99)04787-5
Keywords:
H\'{e}non-like strange attractor,
transversal homoclinic point
Received by editor(s):
January 9, 1997
Received by editor(s) in revised form:
September 30, 1997
Posted:
February 18, 1999
Additional Notes:
The author was partially supported by IMPA, TWAS and NSF of China and Jiangsu and ``Nonlinear Science" Basic Project
Communicated by:
Mary Rees
Copyright of article:
Copyright
1999,
American Mathematical Society
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