In the present paper we study the structure of discrete semi-dynamical system on a set X without any kind of topological structure.
In the first section we do not impose any structure on the set x. Some results then obta ined relative to the c lassification of solutions and to the invariance ot subsets.
In the second section we assume X is a partially ordered set. This allows us to introduce the weak notions which are adequate for systems wit hout uniqueness. Ot particular interest in the characterization of the weak positive invariance presented here.
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