%0 Journal Article
%A Giraldo, A.
%A Rodríguez Sanjurjo, José Manuel
%T Morse-Smale equations of non-saddle decompositions
%D 2004
%@ 0166-8641
%U https://hdl.handle.net/20.500.14352/50157
%X The notion of a non-saddle decomposition of a compact ANR is introduced. This notion extends that of a an attractor-repeller pair. Some cohomological properties of non-saddle decompositions are studied. In particular, some inequalities in the spirit of the Morse-Smale equations for attractor-repeller pairs are obtained. These inequalities involve the ranks of the cohomological Conley index and also of a new cohomological invariant introduced here. The notion of a cyclic Morse decomposition is also introduced and it is proved that this kind of decomposition admits filtrations by non-saddle sets. Finally, these filtrations are used to obtain Morse-Smale equations that generalize those of a Morse decomposition.
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