Giraldo, A.Rodríguez Sanjurjo, José Manuel2023-06-202023-06-2020040166-864110.1016/j.topol.2003.08.018https://hdl.handle.net/20.500.14352/50157International Conference on Topology and Its Applications, SEP 02-09, 2000, Ohrid, MACEDONIAThe 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.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0166864103003353http://www.sciencedirect.com/restricted access514515.1Dynamical systemIsolated setNon-saddle setNon-saddle filtrationCyclic Morse decompositionShapeGeometríaTopología1204 Geometría1210 Topología