标题： 柯普曼空间中的变星光曲线 显示英文标题

标题： Variable Star Light Curves in Koopman Space

摘要： 我们首次将基于Koopman理论的数据驱动技术应用于变星的动力系统分析。 我们重点关注银河球状星团半人马座$\omega$中的RRLyrae型变星光变曲线。 因此，这些光变曲线可以由少量的复特征值来概括，这些特征值对应于振荡或衰减的动力学模式。 我们发现RRc次型变星可以用更少的$\approx 8$个特征值来概括，而RRab则需要相对更多的$\approx 12$个。 这一结果可用于分类，并反映了RRc光变曲线的简单结构。 随后，我们研究了由于泽拉斯基-布拉兹霍效应导致长期变化的变星，发现随着时间推移，相关特征值发生了变化，这可能对理解该效应的物理意义有重要意义。 显示英文摘要

摘要： We present the first application of data-driven techniques for dynamical system analysis based on Koopman theory to variable stars. We focus on light curves of RRLyrae type variables, in the Galactic globular cluster $\omega$ Centauri. Light curves are thus summarized by a handful of complex eigenvalues, corresponding to oscillatory or fading dynamical modes. We find that variable stars of the RRc subclass can be summarized in terms of fewer ($\approx 8$) eigenvalues, while RRab need comparatively more ($\approx 12$). This result can be leveraged for classification and reflects the simpler structure of RRc light curves. We then consider variable stars displaying secular variations due to the Tseraskaya-Blazhko effect and find a change in relevant eigenvalues with time, with possible implications for the physical interpretation of the effect.