初等元胞自动机：有限周期实现的Koopman算子的谱性质
Elementary cellular automata: spectral properties of Koopman operator for finite periodic realizations
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中文总结 AI 辅助
本文研究初等元胞自动机有限周期实现的Koopman算子的谱，提出其谱的刻画并完成谱分类，为后续研究无限实现的对应算子谱奠定基础。
中文摘要 AI 辅助
本文研究与初等元胞自动机的有限周期实现相关联的Koopman算子，这些算子的谱包含了底层动力系统的各种性质，且与任何初始条件无关。文中提出了这些谱的一种刻画，进而对所有初等元胞自动机进行了谱分类，该工作被视为研究初等元胞自动机无限实现的Koopman算子谱的初步步骤。
英文摘要
In this paper we study Koopman operators associated with finite periodic realizations of elementary cellular automata. The spectra of these operators encompass various properties of the underlying dynamical systems, independently of any initial condition. A characterization of these spectra is proposed, leading to a spectral classification of all elementary cellular automata. This work is thought as a preliminary step for studying the spectra of Koopman operators for infinite realizations of elementary cellular automata.
