%0 Journal Article
%A Giraldo, A.
%A Alonso Morón, Manuel
%A Romero Ruiz Del Portal, Francisco
%A Rodríguez Sanjurjo, José Manuel
%T Some duality properties of non-saddle sets
%D 2001
%@ 0166-8641
%U https://hdl.handle.net/20.500.14352/57293
%X 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.
%~