Localization of Invariant Compacts in Discrete Systems

The functional method of localization of invariant compact sets for discrete dynamical systems is considered, with whose help the one-dimensional logistic system and twodimensional Cathala system are studied. The compact localization of positively-invariant compact sets of these systems is constructed. It is shown for both systems that the union of negatively-invariant compact sets coincides with the phase space of the system.