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Motivated by the study of the recurrent orbits in a Morse set of a Morsedecomposition, we introduce the concept of Morse predecomposition of anisolated invariant set in the setting of combinatorial and classical dynamicalsystems. We prove that a Morse predecomposition indexed by a poset is a Morsedecomposition and we show how a Morse predecomposition may be condensed back toa Morse decomposition.

Morse predecomposition of an ivariant set