论文标题
局部分析和正式向量领域的中心化和归一化器
Centralizers and normalizers of local analytic and formal vector fields
论文作者
论文摘要
我们使用Poincaré-Dulac正常形式的理论研究了非平稳地点的局部分析或形式差异系统的局部分析或形式差异系统的归一化器的结构。我们的主要结果与正式案件有关。当线性化的中央器具有有限的尺寸，并且总体上较低的估计值时，我们获得了中央器和归一化量之间的关系的描述。对于一类杰出的线性矢量场（足够大的线性矢量场），我们获得了centralizer在通用情况下的相应正常形式的准确表征。此外，鉴于它们与正常化的关系，我们讨论了雅各比乘数乘数，并获得了几类矢量字段的存在标准和不存在的结果。
We investigate the structure of the centralizer and the normalizer of a local analytic or formal differential system at a nondegenerate stationary point, using the theory of Poincaré-Dulac normal forms. Our main results are concerned with the formal case. We obtain a description of the relation between centralizer and normalizer, sharp dimension estimates when the centralizer of the linearization has finite dimension, and lower estimates for the dimension of the centralizer in general. For a distinguished class of linear vector fields (which is sufficiently large to be of interest) we obtain a precise characterization of the centralizer for corresponding normal forms in the generic case. Moreover, in view of their relation to normalizers, we discuss inverse Jacobi multipliers and obtain existence criteria and nonexistence results for several classes of vector fields.
