A mobile agent system network is, in our definition, a dynamical system where so called agent servers are loosely coupled. In such an environment (mobile) agents may offer and consume services and act on behalf of a (human) user. This paper characterizes the dynamical behavior of such a network. Aspects of dynamical behavior are discussed, dynamical components are characterized, and a ”cartography” method to handle dynamics is introduced. The resulting ”maps” can be used to support the autonomy of agents by calculating itineraries and suggest migration strategies. The application of the map described in this paper is based on one of our current research projects in the context of the mobile agent system Tracy.