Fractal capacities and iterated function systems

Анотація

Iterated function systems are defined for inclusion hyperspaces and capacities, and counterparts of classical theorems on attractors, namely the fixed point theorem, the continuity with respect to a contraction, the collage and anti-collage theorems, are proved. Self-similar random capacities are also defined, and their properties, analogous to properties of random self-similar measures, are investigated.