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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 $M$.
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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