On the topology of the boundary of a basin of attraction
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- by J. J. Sánchez-Gabites and J. M. R. Sanjurjo PDF
- Proc. Amer. Math. Soc. 135 (2007), 4087-4098 Request permission
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 $M$.References
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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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 4087-4098
- MSC (2000): Primary 54H20, 55P55, 58F12
- DOI: https://doi.org/10.1090/S0002-9939-07-08972-1
- MathSciNet review: 2341961