Topological stability of iterated function systems

Abstract: We study Iterated Function Systems (IFS) with compact parameter space. We show that the compactness of the phase space permits us to obtain a natural metric on the space of IFS which extends $C^0$-topology to the space of IFS. We then use this metric to define topological stability and to prove that in this context the classical results saying that shadowing property is a necessary condition for topological stability and that shadowing property together with expansiveness are sufficient conditions.

For a proof of these statements, in fact we use a stronger type of shadowing property which we show to be different than the standard one.

This is joint work with Alexander Arbieto.

dynamical systems

Audience: researchers in the topic

Dynamical systems seminar at the Jagiellonian University