论文标题
差异性及其本地正常形式的完全可整合性
Complete integrability of diffeomorphisms and their local normal forms
论文作者
论文摘要
在本文中，我们考虑了在固定点（例如，$ \ mathbb {k}^n $（$ \ Mathbb {k} = \ Mathbb {c} $或$ \ mathbb {r} $）的固定点（例如$ \ mathbb {k}^n $（$ \ mathbb {k}^n $的起源））的正常形式问题。我们定义了这样一个家庭的综合性概念。我们提供足够的条件，以确保如果初始差异性是分析性的（分别平滑），则可以通过分析（分析平滑）转化将这种可集成的家族转化为正常形式。
In this paper, we consider the normal form problem of a commutative family of germs of diffeomorphisms at a fixed point, say the origin, of $\mathbb{K}^n$ ($\mathbb{K}=\mathbb{C}$ or $\mathbb{R}$). We define a notion of integrability of such a family. We give sufficient conditions which ensure that such an integrable family can be transformed into a normal form by an analytic (resp. a smooth) transformation if the initial diffeomorphisms are analytic (resp. smooth).
