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Some duality properties of non-saddle sets

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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


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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
Uncontrolled Keywords:Dynamical system; isolated set; non-saddle set; shape
Subjects:Sciences > Mathematics > Topology
ID Code:15410
Deposited On:29 May 2012 11:35
Last Modified:12 Dec 2018 15:13

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