Notes on Hypercyclicity of Composition Operator on the Weighted Dirichlet Spaces

In this paper, the hypercyclic behavior of multiples of composition operators induced by linear fractional self-maps of unit disk on the weighted Dirichlet spaces 𝒟^p_α will be presented. Using the classification of linear fractional self-maps, we show that composition operators exhibit strikingly diverse types of hypercyclic behavior. Furthermore, Colonna and Martínez-Avebdaño raised the open question: When p-2<α

3 . In this paper, we show that under the condition p-2<α

1 .