Multivalued maps in stability theory of dynamical systems

Summary Multivalued maps like orbit, limit set, prolongations etc., are an useful tool in Dynamical Systems theory. In this work we develop a calculus for multivalued maps associated with a dynamical system. Then we give general definitions of stability and attraction of a compact set with respect to a multivalued map. On the basis of our calculus, we obtain several characterizations of stability and attraction, which generalise well known classical theorems. Such a general theory is applied to total stability of diffentiable dynamical systems. The equivalence among several approaches to total stability is established.