Barge, HéctorRodríguez Sanjurjo, José Manuel2023-06-172023-06-1720171040-729410.1007/s10884-017-9569-3https://hdl.handle.net/20.500.14352/17653This paper is devoted to the study of some aspects of the stability theory of flows. In particular, we study Morse decompositions induced by non-saddle sets, including their corresponding Morse equations, attractor-repeller splittings of non-saddle sets and bifurcations originated by implosions of the basin of attraction of asymptotically stable fixed points. We also characterize the non-saddle sets of the plane in terms of the Euler characteristic of their region of influence.engjournal articlehttp://link.springer.com/article/10.1007/s10884-017-9569-3http://link.springer.com/restricted access517.9Attractor-repeller splittingBifurcationConley indexMorse decompositionNon-saddle setEcuaciones diferenciales1202.07 Ecuaciones en Diferencias