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Complete Integrability of Diffeomorphisms and Their Local Normal Forms

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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 \(\mathbb {K}^n (\mathbb {K}={\mathbb {C}}\text {~or~} {\mathbb {R}})\). 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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Authors and Affiliations

  1. Beijing International Center for Mathematical Research, Peking University, Beijing, China

    Kai Jiang

  2. Laboratoire J.A. Dieudonné, UMR CNRS 7351, Université Côte d’Azur, Nice, France

    Kai Jiang & Laurent Stolovitch

Authors
  1. Kai Jiang
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  2. Laurent Stolovitch
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Correspondence to Laurent Stolovitch.

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A la mémoire de Walter

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This work has been supported by the French government, through the UCAJEDI Investments in the Future project managed by the National Research Agency (ANR) with the reference Number ANR-15-IDEX-01 and by ANR project BEKAM with the reference number ANR-15-CE40-0001-03.

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Jiang, K., Stolovitch, L. Complete Integrability of Diffeomorphisms and Their Local Normal Forms. J Dyn Diff Equat 33, 1179–1201 (2021). https://doi.org/10.1007/s10884-020-09902-y

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  • DOI: https://doi.org/10.1007/s10884-020-09902-y

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