Topology and dynamics of unstable attractors

Volume 197 / 2007

M. A. Morón, J. J. Sánchez-Gabites, J. M. R. Sanjurjo Fundamenta Mathematicae 197 (2007), 239-252 MSC: 54H20, 55P55, 37C70, 37B30. DOI: 10.4064/fm197-0-11

Abstract

This article aims to explore the theory of unstable attractors with topological tools. A short topological analysis of the isolating blocks for unstable attractors with no external explosions leads quickly to sharp results about their shapes and some hints on how Conley's index is related to stability. Then the setting is specialized to the case of flows in $\mathbb{R}^n$, where unstable attractors are seen to be dynamically complex since they must have external explosions.

Authors

  • M. A. MorónFacultad de Matemáticas
    Universidad Complutense
    28040 Madrid, Spain
    e-mail
  • J. J. Sánchez-GabitesFacultad de Matemáticas
    Universidad Complutense
    28040 Madrid, Spain
    e-mail
  • J. M. R. SanjurjoFacultad de Matemáticas
    Universidad Complutense
    28040 Madrid, Spain
    e-mail

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