, Volume 19, Issue 1, pp 181-198
Date: 14 Jul 2006

Morse Decomposition of Semiflows on Topological Spaces

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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.