Stability in terms of two measures for set difference equations in space conv (Rn)

The set of trajectories for discrete dynamical systems (DDS) in the space R-n is investigated. These sets are the solutions for difference equations in a metric space conv (R-n) (space of nonempty convex compacts with the Hausdorff metric). On the basis of the comparison principle the general theorems on stability in terms of two measures were established. Applying the Minkowskij theory of mixed volumes, for some classes of nonlinear DDS in space conv (R-3) the finite-dimensional comparison systems were constructed. The stability in terms of two measures and Lyapunov stability of fixed points for DDS in space conv (R-3) were studied. The examples of studies of certain dynamical systems were given to illustrate the effectiveness of obtained results.