Disjoint strong transitivity of composition operators

Noureddine Karim; Otmane Benchiheb; Mohamed Amouch

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arXiv · 2205.10638

Disjoint strong transitivity of composition operators

Noureddine Karim·Otmane Benchiheb·Mohamed Amouch

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Abstract

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 $ϕ_1,...,ϕ_N$.

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BibTeX RIS

Noureddine Karim, Otmane Benchiheb, Mohamed Amouch. 2022-11-28. Disjoint strong transitivity of composition operators. https://arxiv.org/abs/2205.10638

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