Doubling Property on Hutchinson Orbits of Some Families of Contractive Similitudes

Abstract

We are interested in the behavior of the dynamical system generated by successive applications of Hutchinson similitudes starting from a metric measure space. We prove that, in the case of families of similitudes with the same contraction ratio, even when no point of the orbit is a doubling space, a gradual doubling property is taking place and the limit point recovers the homogeneity property.