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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The transversal homoclinic points
are dense in the codimension-1
Hénon-like strange attractors


Author: Yongluo Cao
Journal: Proc. Amer. Math. Soc. 127 (1999), 1877-1883
MSC (1991): Primary 58F11, 58F12
Published electronically: February 18, 1999
MathSciNet review: 1487360
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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 $.


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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: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 1999 American Mathematical Society