Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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
MathSciNet review: 1487360
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We consider the codimension-1 Hénon-like strange attractors $\Lambda $. We prove that the transversal homoclinic points are dense in $\Lambda $, and that hyperbolic periodic points are dense in $\Lambda $. Moreover the hyperbolic periodic points that are heteroclinically related to the primary fixed point ( transversal intersection of stable and unstable manifolds) are dense in $\Lambda $.


References:

1.
M.Benedicks & L.Carleson, The dynamics of the Hénon map, Ann. Math. 133 (1991), 73-169. MR 92d:58116

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

5.
J.Palis & F.Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge Press, 1993. MR 94h:58129

6.
M.Viana, Strange attractors in higher dimensions, Bull.Braz.Math.Soc. 24 (1993), 13-62. MR 94k:58093


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58F11, 58F12

Retrieve articles in all Journals with MSC (1991): 58F11, 58F12


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




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia