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

 

On the topology of the boundary of a basin of attraction


Authors: J. J. Sánchez-Gabites and J. M. R. Sanjurjo
Journal: Proc. Amer. Math. Soc. 135 (2007), 4087-4098
MSC (2000): Primary 54H20, 55P55, 58F12
Published electronically: September 12, 2007
MathSciNet review: 2341961
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Abstract: Suppose $ \varphi : M \times \mathbb{R} \longrightarrow M$ is a continuous flow on a locally compact metrizable space $ M$ and $ K$ is an (asymptotically stable) attractor. Let $ D = \partial \mathcal{A}(K)$ be the boundary of the basin of attraction of $ K$. In the present paper it will be shown how the Conley index of $ D$ plays an important role in determining the topological nature of $ D$ and allows one to obtain information about the global dynamics of $ \varphi$ in $ M$.


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Additional Information

J. J. Sánchez-Gabites
Affiliation: Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
Email: jajsanch@mat.ucm.es

J. M. R. Sanjurjo
Affiliation: Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
Email: jose_sanjurjo@mat.ucm.es

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08972-1
PII: S 0002-9939(07)08972-1
Received by editor(s): March 22, 2006
Received by editor(s) in revised form: September 15, 2006
Published electronically: September 12, 2007
Additional Notes: The authors were partially supported by DGI
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.