General hyperbolicity conditions for set-valued mappings

We give a definition of hyperbolicity for dynamical systems generated by set-valued mappings of general form in terms of local selectors. It is shown that a system hyperbolic in this sense has the shadowing and inverse shadowing properties. It is also shown that the hyperbolicity property holds true for a certain class of set-valued mappings in which images of points are convex polytopes. Bibl. – 13 titles.