  Motivated by the study of the recurrent orbits in a Morse set of a Morse
decomposition, we introduce the concept of Morse predecomposition of an
isolated invariant set in the setting of combinatorial and classical dynamical
systems. We prove that a Morse predecomposition indexed by a poset is a Morse
decomposition and we show how a Morse predecomposition may be condensed back to
a Morse decomposition.
