Rodríguez Sanjurjo, José Manuel2023-06-202023-06-2020120022-039610.1016/j.jde.2012.01.036https://hdl.handle.net/20.500.14352/42345We study the internal structure of the global attractor of a uniformly persistent flow. We show that the restriction of the flow to the global attractor has duality properties which can be expressed in terms of certain attractor-repeller decompositions. We also study some natural Morse decompositions of the flow and calculate their Morse equations. These equations provide necessary and sufficient conditions for the existence of attractors with the shape of S-1 or such that their suspension has spherical shape.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022039612000605http://www.sciencedirect.com/restricted access514515.1Uniform persistenceAttractorRepellerRobustnessContinuationMorse equationsShapeGeometríaTopología1204 Geometría1210 Topología