A Furstenberg family \(\mathcal{F}\) is a collection of infinite subsets ofthe set of positive integers such that if \(A\subset B\) and \(A\in \mathcal{F}\), then \(B\in \mathcal{F}\). For aFurstenberg family \(\mathcal{F}\), an operator \(T\) on a topological vector space \(X\) is said tobe \(\mathcal{F}\)-transitive provided that for each non-empty open subsets \(U\), \(V\) of \(X\) the set\(\{n \in \mathbb{N}: T^n (U) \cap V \neq\emptyset\}\) belongs to \(\mathcal{F}\). In this paper, we characterize the \(\mathcal{F}\)-transitivityof composition operator \(C_\phi\) on the space \(H(\Omega)\) of holomorphic functionson a domain \(\Omega\subset \mathbb{C}\) by providing a necessary and sufficient condition in terms ofthe symbol \(\phi\).

Furstenberg 族\(\mathcal{F}\)是一组正整数的无限子集的集合，如果\(A\subset B\)和\(A\in \mathcal{F}\)，则\ (B\in \mathcal{F}\)。对于 aFurstenberg 族\(\mathcal{F}\)，拓扑向量空间\(X\)上的算子\(T \)被称为\(\mathcal{F}\) -传递性，前提是对于每个非空开子集\(U\) , \(V\) of \(X\)集合\(\{n \in \mathbb{N}: T^n (U) \cap V \neq\emptyset\} \)属于\(\mathcal{F}\). 在本文中，我们在域\(\Omega\subset )的全纯函数的空间\(H(\Omega)\)上刻画了\(\mathcal{F}\) -组合算子\(C_\phi \)的传递性\mathbb{C}\)通过提供符号\(\phi\) 的充分必要条件。