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

We study tensor products of strongly continuous semigroups on Banach spaces that satisfy the hypercyclicity criterion, the recurrent hypercyclicity criterion or are chaotic.

We study hypercyclicity of Toeplitz operators in the Hardy space H2(D) with symbols form R(z‾)+φ(z), where R is a rational function and φ∈H∞(D). relate this problem to cyclicity certain families functions for analytic give new sufficient conditions based on deep results B. Solomyak.