论文标题
部分可观测时空混沌系统的无模型预测
Geometric aspects of Young Integral: decomposition of flows
论文作者
论文摘要
在本文中，我们研究由$α$-Hölder轨迹驱动的年轻微分方程（YDE）产生的动力学的几何方面，其$α\ in（1/2，1）$。我们在这种低规律性的情况下介绍了许多特性和几何结构：年轻的ITôDemortical公式，主纤维束的水平升力，平行运输，协变量衍生物，发展和反开发等。我们这里的主要应用是YDES产生的流量的几何分解，该流量是根据互补分布（是否可以整合）产生的差异性产生的。这种分解的存在证明是基于Castrequini和Catuogno证明的$α$ -H {Ö} lder路径的年轻Itô-Kunita公式（Chaos Solitons fractals，2022年）。
In this paper we study geometric aspects of dynamics generated by Young differential equations (YDE) driven by $α$-Hölder trajectories with $α\in (1/2, 1)$. We present a number of properties and geometrical constructions on this low regularity context: Young Itô geometrical formula, horizontal lift in principal fibre bundles, parallel transport, covariant derivative, development and anti-development, among others. Our main application here is a geometrical decomposition of flows generated by YDEs according to diffeomorphisms generated by complementary distributions (integrable or not). The proof of existence of this decomposition is based on an Young Itô-Kunita formula for $α$-H{ö}lder paths proved by Castrequini and Catuogno (Chaos Solitons Fractals, 2022).
