Invariant measures for place-dependent idempotent iterated function systems

We study the set of invariant idempotent probabilities for place-dependent idempotent iterated function systems defined in compact metric spaces. Using well-known ideas from dynamical systems, such as the Mañé potential and the Aubry set, we provide a complete characterization of the densities of such idempotent probabilities. As an application, we provide an alternative formula for the attractor of a class of fuzzy iterated function systems.