Strong transitivity of composition operators.

A Furstenberg family F is a collection of infinite subsets ofthe set of positive integers such that if A ⊂ B and A ∈ F , then B ∈ F . For aFurstenberg family F , an operator T on a topological vector space X is said tobe F -transitive provided that for each non-empty open subsets U , V of X the set { n ∈ N : T n (U) ∩ V ≠ ∅ } belongs to F . In this paper, we characterize the F -transitivityof composition operator C ϕ on the space H (Ω) of holomorphic functionson a domain Ω ⊂ C by providing a necessary and sufficient condition in terms ofthe symbol ϕ . [ABSTRACT FROM AUTHOR]