论文标题
分析动态中的等效问题，价格为1美元
The equivalence problem in analytic dynamics for $1$-resonance
论文作者
论文摘要
在单个点附近的坐标分析变化下，分析系统结合或轨道等效的两种细菌何时？回答的一种方法是使用正常形式。但是，有大量的动态系统，将坐标变为正常形式。在本文中，我们讨论了奇异性的情况下，标准化转换为$ k $ - 可言，因此可以提供模量空间。我们解释了这些奇异性的常见几何特征，并表明对它们展开的研究允许了解奇异性本身，以及几何障碍物以融合归一化转化的趋势。我们还提供了一些模量$ K $ - 参数家庭，这些空间展现了这种奇异性。
When are two germs of analytic systems conjugate or orbitally equivalent under an analytic change of coordinates in the neighborhood of a singular point? A way to answer is to use normal forms. But there are large classes of dynamical systems for which the change of coordinates to a normal form diverges. In this paper we discuss the case of singularities for which the normalizing transformation is $k$-summable, thus allowing to provide moduli spaces. We explain the common geometric features of these singularities, and show that the study of their unfoldings allows understanding both the singularities themselves, and the geometric obstructions to convergence of the normalizing transformations. We also present some moduli spaces for generic $k$-parameter families unfolding such singularities.
