Proceedings of the American Mathematical Society

Author(s): J. J. Sánchez-Gabites; J. M. R. Sanjurjo
Journal: Proc. Amer. Math. Soc. 135 (2007), 4087-4098.
MSC (2000): Primary 54H20, 55P55, 58F12
Posted: September 12, 2007
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Abstract: Suppose $\varphi : M \times \mathbb{R} \longrightarrow M$ is a continuous flow on a locally compact metrizable space

and

is an (asymptotically stable) attractor. Let $D = \partial \mathcal{A}(K)$ be the boundary of the basin of attraction of

. In the present paper it will be shown how the Conley index of

plays an important role in determining the topological nature of

and allows one to obtain information about the global dynamics of $\varphi$ in

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54H20, 55P55, 58F12

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: 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
Posted: September 12, 2007
Additional Notes: The authors were partially supported by DGI
Communicated by: Alexander N. Dranishnikov
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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