Uniformly almost periodic points (Q674672)

We introduce a new level on recurrent motion in discrete semi-dynamical systems, i.e. uniformly almost periodic (U.A.P.) points. For a U.A.P. point we prove that, when the map is restricted on its \(\omega\)-limit set, it is a homeomorphism, strictly ergodic and with zero-topological entropy. Moreover, we give the \(\omega\)-limit set a description of a compact topological group structure.