Hypercyclic property of weighted composition operators

Abstract

Abstract. In the present paper we investigate conditions under which a holomorphic self-map of the open unit disk induces a hypercyclic weighted composition operator in the space of holomorphic functions.

Dynamics of Hyperbolic Weighted Composition Operators

“…Now we apply the techniques used in [7]. Since ψ is hyperbolic, thus 0 < d(w) < 1 and by Theorem 1.2 we have…”

Dynamics of a Special Combination of Weighted Composition Operators on Hilbert Function Spaces

“…Now by the same method used in [4] we can see that: L n k z → 0, S n k y → 0, LS(k y ) = k y for all k z ∈ H 1 and k y ∈ H 2 . Therefore L satisfies the hypothesis of hypercyclicity criterion and so the proof is complete.…”

Chaotic Property of Weighted Composition Operators

“…□ Definition 2.3. For any w ∈ U and positive real number β, we denote by Lip β (w), the class of holomorphic functions φ satisfying We extend these results from [13] in two directions: we eliminate the requirement that |φ(w)| = 1, and, in the parabolic case, we allow ψ be any map of parabolic-automorphic type (but we do require β = 2).…”