Euroattractor: a brief introduction to Iterated Function Systems

In this work we propose a definition of an Euroattractor: an attracting invariant measure of a certain iterated functions system (IFS). An IFS is defined by specifying a set of functions, defined in subsets of R^N or in a classical phase space, which act randomly on the initial point, so it may be considered as a generalization of the notion of classical dynamical system. If the functions are sufficiently contracting, there exists an invariant measure of the system, often concentrated on a fractal set. We investigate invariant measures of a certain class of generalized or weakly contracting IFS's.