Giraldo, A.Alonso Morón, ManuelRomero Ruiz Del Portal, FranciscoRodríguez Sanjurjo, José Manuel2023-06-202023-06-202001-06-29Giraldo, 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)00017-1.0166-864110.1016/S0166-8641(00)00017-1https://hdl.handle.net/20.500.14352/57293We 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.engjournal articlehttps//doi.org/10.1016/S0166-8641(00)00017-1http://www.sciencedirect.com/science/article/pii/S0166864100000171open access515.143517.938Dynamical systemIsolated setNon-saddle setShapeTopología1210 Topología