About the relationships between some characteristics superhomogeneous and subhomogeneous mappings

Discusses the properties of the matching between classes subhomogeneous and superhomogeneous mappings implemented by the introduction of so-called conjugated mapping. The mapping conjugated with respect to subhomogeneous (resp. superhomogeneous) mapping is superhomogeneous (resp. subhomogeneous). Examines the relationship of certain characteristics of mutually conjugate representations, such as the existence of positive fixed points and the structure of the set of fixed points, also irreducibility of mappings, etc.