通过Jordan-Chevalley分解嵌入光滑的形式同态
Embedding smooth and formal diffeomorphisms through the Jordan-Chevalley decomposition
摘要：
在[Xiang Zhang，The embedding flows of $C^{\infty}$ hyperbolic hyperbolic morphisms，J.微分方程250（2011），no. 5，2283-2298]中，Zhang证明了特征值弱非共振的任何局部光滑双曲型超同态嵌入光滑向量场的流中。利用代数群上的Jordan-Chevalley分解和指数算子的性质给出了这一结果的一个新的、更简单和更概念化的证明.我们刻画了双曲光滑（分别为形式上的）嵌入在光滑（或光滑）中的同构。形式）流动。我们引入了一个准则，表明弱共振的存在下，一个单同态加上两个自然条件意味着它是不可嵌入的。这解决了张的一个猜想。该准则是最优的，我们给出了一个方法，如果我们去除任何条件，我们可以构造具有弱共振的可嵌入的自同态。
英文摘要：
In [Xiang Zhang, The embedding flows of $C^{\infty}$ hyperbolic diffeomorphisms, J. Differential Equations 250 (2011), no. 5, 2283-2298] Zhang proved that any local smooth hyperbolic diffeomorphism whose eigenvalues are weakly nonresonant is embedded in the flow of a smooth vector field. We present a new, simpler and more conceptual proof of such result using the Jordan-Chevalley decomposition in algebraic groups and the properties of the exponential operator. We characterize the hyperbolic smooth (resp. formal) diffeomorphisms that are embedded in a smooth (resp. formal) flow. We introduce a criterium showing that the presence of weak resonances for a diffeomorphism plus two natural conditions imply that it is not embeddable. This solves a conjecture of Zhang. The criterium is optimal, we provide a method to construct embeddable diffeomorphisms with weak resonances if we remove any of the conditions.
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