论文标题
部分可观测时空混沌系统的无模型预测
The Poisson linearization problem for $\mathfrak{sl}_2(\mathbb{C})$. Part II: The Nash-Moser method
论文作者
论文摘要
这是两篇论文中的第二篇，其中我们证明了CONN的线性化定理的Lie代数$ \ Mathfrak {SL} _2（\ Mathbb {C}）\ Simeq \ Mathfrak {So}（So}（3,1）$。也就是说，我们表明的任何泊松结构的线性近似为零的结构与与$ \ mathfrak {sl} _2 _2（\ Mathbb {c}）$相关的泊松结构是同构的。在第一部分中，我们计算了与$ \ mathfrak {sl} _2（\ Mathbb {C}）$相关的Poisson共同体，并为原始poisson copplect构建了有限的同型操作员。在第二部分中，我们获得了线性化结果，该结果适用于更一般的Lie代数类别。对于证明，我们开发了一种NASH-MOSER方法，用于在某个时刻平坦的功能。
This is the second of two papers, in which we prove a version of Conn's linearization theorem for the Lie algebra $\mathfrak{sl}_2(\mathbb{C})\simeq \mathfrak{so}(3,1)$. Namely, we show that any Poisson structure whose linear approximation at a zero is isomorphic to the Poisson structure associated to $\mathfrak{sl}_2(\mathbb{C})$ is linearizable. In the first part, we calculated the Poisson cohomology associated to $\mathfrak{sl}_2(\mathbb{C})$, and we constructed bounded homotopy operators for the Poisson complex of multivector fields that are flat at the origin. In this second part, we obtain the linearization result, which works for a more general class of Lie algebras. For the proof, we develop a Nash-Moser method for functions that are flat at a point.
