Disjoint strong transitivity of composition operators

Abstract

A Furstenberg Family F is a collection of infinite subsets of the set of positive integers such that if A ⊂ B and A ∈ F , then B ∈ F . For a Furstenberg family F , finitely many operators T 1 , ..., T N acting on a common topological vector space X are said to be disjoint F -transitive if for every non-empty open subsets U 0 , ..., U N of X the setIn this paper, depending on the topological properties of Ω, we characterize the disjoint F -transitivity of N ≥ 2 composition operators C φ 1 , . . . , C φ N acting on the space H(Ω) of holomorphic maps on a domain Ω ⊂ C by establishing a necessary and sufficient condition in terms of their symbols φ 1 , ..., φ N .2010 Mathematics Subject Classification. 47A16, 46A99.