### Impacto

Giraldo, A. and Morón, Manuel A. and Romero Ruiz del Portal, Francisco and Rodríguez Sanjurjo, José Manuel
(2001)
*Some duality properties of non-saddle sets.*
Topology and its Applications, 113
(1-3).
pp. 51-59.
ISSN 0166-8641

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Official URL: http://www.sciencedirect.com/science/article/pii/S0166864100000171

## Abstract

We show in this paper that the class of compacts that call be isolated non-saddle sets of flows in ANRs is precisely the class of compacta with polyhedral shape. We also prove-reinforcing the essential role played by shape theory in this setting-that the Conley index of a regular isolated non-saddle set is determined, in certain cases, by its shape. We finally introduce and study the notion of dual of a non-saddle set. Examples of compacta related by duality are attractor-repeller pairs. We use the complement theorems in shape theory to prove that the shape of the dual set is determined by the shape of the original non-saddle set.

Item Type: | Article |
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Uncontrolled Keywords: | Dynamical system; isolated set; non-saddle set; shape |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 15410 |

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Deposited On: | 29 May 2012 11:35 |

Last Modified: | 06 Feb 2014 10:24 |

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