Morse Decomposition of Semiflows on Topological Spaces
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- Patrão, M. J Dyn Diff Equat (2007) 19: 181. doi:10.1007/s10884-006-9033-2
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This paper studies Morse decompositions of discrete and continuous-time semiflows on compact Hausdorff topological spaces. We extend two classical results which are well-known facts for flows on compact metric spaces: the characterization of the Morse decompositions through increasing sequences of attractors and the existence of Lyapunov functions.