In this paper we introduce and study the notion of hypercyclicity for iterated function systems (IFS) operators. We prove that a linear IFS, implies sensitivity if an IFS is abelian, then also multi-sensitivity hence thick sensitivity. give some equivalent conditions as well weakly mixing

Abstract We consider the iterated function system Fn = fn ◦ . . . ◦ f2 ◦ f1 formed from the holomorphic functions in the family H(∆,Ω). The analog of stable behavior for such systems is that the limit functions be constant. We prove that a necessary and sufficient condition for stable behavior for all iterated function systems formed from H(∆, Ω) is that Ω be a proper subset of ∆. We also prove...

An iterated function system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum IFS (QIFS), where functions act randomly with prescribed probabilities in the Hilbert space. In a more general setting, a QIFS consists of completely positive maps acting in the space of density operators. This...