Morphisms for Semi–dynamical Systems

Introduction. The semi–dynamical systems were introduced in the framework of the axiomatic potential theory by H m i s s i [5] and, in the more general form used in this note, by B u c u r – B e z z a r g a [1], [2]. The present paper is a natural continuation of [8] and represents the printed form of the technical report [9]. The notion of morphism was introduced in potential theory in [6], see also [3]. Since not every semi– dynamical system is associated with a H–cone, the definitions of the notions of a morphism and of a H–aplication must be adapted accordingly. The main result of this paper (Th. 4.1.) characterizes the H–aplications among the morphisms of semi–dynamical systems. Of course, this characterization is different from the one given in the framework of H–cones, as the minimum of two excessive functions is replaced with their product.