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COMPLETE INTEGRABILITY OF DIFFEOMORPHISMS AND THEIR LOCAL NORMAL FORMS

Abstract : 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).
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https://hal.archives-ouvertes.fr/hal-02902652
Contributor : Laurent Stolovitch <>
Submitted on : Monday, July 20, 2020 - 10:48:43 AM
Last modification on : Wednesday, October 14, 2020 - 4:24:41 AM

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  • HAL Id : hal-02902652, version 1
  • ARXIV : 2007.10630

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Kai Jiang, Laurent Stolovitch. COMPLETE INTEGRABILITY OF DIFFEOMORPHISMS AND THEIR LOCAL NORMAL FORMS. 2020. ⟨hal-02902652⟩

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