论文标题
构图操作员的强大传递性
Disjoint strong transitivity of composition operators
论文作者
论文摘要
Furstenberg家族$ \ MATHCAL {F} $是一组正整数的无限子集的集合，因此，如果$ a \ subset b $和$ a \ in \ Mathcal {f} $，那么$ b \ in \ Mathcal {f} $。对于一个furstenberg family $ \ mathcal {f} $，有限的许多操作员$ t_1，...，t_n $作用在常见的拓扑矢量空间上$ x $是不相关的$ \ nathcal {f} $ - 如果对于每个非空的开放式子集$ u_0，... \ Mathbb {n}：\ u_0 \ cap t_1^{ - n}（u_1）\ cap ... \ cap t_n^{ - n} { - n}（u_n）\ neq \ neq \ emberyset \} $ In this paper, depending on the topological properties of $Ω$, we characterize the disjoint $\mathcal{F}$-transitivity of $N\geq2$ composition operators $C_{ϕ_1},\ldots,C_{ϕ_N}$ acting on the space $H(Ω)$ of holomorphic maps on a domain $Ω\subset \ Mathbb {C} $通过根据其符号$ ϕ_1，...，ϕ_n $建立必要且充分的条件。
A Furstenberg family $\mathcal{F}$ is a collection of infinite subsets of the set of positive integers such that if $A\subset B$ and $A\in \mathcal{F}$, then $B\in \mathcal{F}$. For a Furstenberg family $\mathcal{F}$, finitely many operators $T_1,...,T_N$ acting on a common topological vector space $X$ are said to be disjoint $\mathcal{F}$-transitive if for every non-empty open subsets $U_0,...,U_N$ of $X$ the set $\{n\in \mathbb{N}:\ U_0 \cap T_1^{-n}(U_1)\cap...\cap T_N^{-n}(U_N)\neq\emptyset\}$ belongs to $\mathcal{F}$. In this paper, depending on the topological properties of $Ω$, we characterize the disjoint $\mathcal{F}$-transitivity of $N\geq2$ composition operators $C_{ϕ_1},\ldots,C_{ϕ_N}$ acting on the space $H(Ω)$ of holomorphic maps on a domain $Ω\subset \mathbb{C}$ by establishing a necessary and sufficient condition in terms of their symbols $ϕ_1,...,ϕ_N$.
