Hypercyclic and chaotic operators in space of functions analytic in domain

We consider the space $H(\Omega)$ of functions analytic in a simply connected domain $\Omega$ in the complex plane equipped with the topology of uniform convergence on compact sets. We study issues on hypercyclicity, chaoticity and frequently hypercyclic for some operators in this space. We prove that a linear continuous operator in $H(\Omega),$ which commutes with the differentiation operator, is hypercyclic. We also show that this operator is chaotic and frequently hypercyclic in $H(\Omega).$