COMPLETE INTEGRABILITY OF DIFFEOMORPHISMS AND THEIR LOCAL NORMAL FORMS

Kai Jiang (1, 2) , Laurent Stolovitch (3)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 BICMR
3 LJAD - Laboratoire Jean Alexandre Dieudonné

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).

Domaines: Systèmes dynamiques [math.DS]

Kai Jiang, Laurent Stolovitch. COMPLETE INTEGRABILITY OF DIFFEOMORPHISMS AND THEIR LOCAL NORMAL FORMS. Journal of Dynamics and Differential Equations, 2020, ⟨10.1007/s10884-020-09902-y⟩. ⟨hal-02902652⟩