Some duality properties of non-saddle sets
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2001
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Elsevier Science
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Giraldo, A., Alonso Morón, M., Romero Ruiz Del Portal, F., Rodríguez Sanjurjo, J. M. «Some Duality Properties of Non-Saddle sets☆☆The Authors Are Supported by DGESIC.» Topology and Its Applications, vol. 113, n.o 1-3, junio de 2001, pp. 51-59. DOI.org (Crossref), https://doi.org/10.1016/S0166-8641(00)00017-1.
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.