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Regul. Chaotic Dyn., 2016, Volume 21, Issue 1, Pages 18–23 (Mi rcd65)  

This article is cited in 1 scientific paper (total in 1 paper)

Local Normal Forms of Smooth Weakly Hyperbolic Integrable Systems

Kai Jiang

Institut de Mathématiques de Jussieu Paris Rive Gauche, Université Paris 7 7050 Bâtiment Sophie Germain, Case 7012, 75205 Paris CEDEX 13, France

Abstract: In the smooth $(C^\infty)$ category, a completely integrable system near a nondegenerate singularity is geometrically linearizable if the action generated by the vector fields is weakly hyperbolic. This proves partially a conjecture of Nguyen Tien Zung [11]. The main tool used in the proof is a theorem of Marc Chaperon [3] and the slight hypothesis of weak hyperbolicity is generic when all the eigenvalues of the differentials of the vector fields at the non-degenerate singularity are real.

Keywords: completely integrable systems, geometric linearization, nondegenerate singularity, weak hyperbolicity

DOI: https://doi.org/10.1134/S1560354716010020

References: PDF file   HTML file

Bibliographic databases:

MSC: 37C05, 37C10, 37C25, 37D05, 37D10, 37J60
Received: 02.04.2015
Accepted:13.08.2015
Language:

Citation: Kai Jiang, “Local Normal Forms of Smooth Weakly Hyperbolic Integrable Systems”, Regul. Chaotic Dyn., 21:1 (2016), 18–23

Citation in format AMSBIB
\Bibitem{Jia16}
\by Kai Jiang
\paper Local Normal Forms of Smooth Weakly Hyperbolic Integrable Systems
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 1
\pages 18--23
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\crossref{https://doi.org/10.1134/S1560354716010020}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3457074}
\zmath{https://zbmath.org/?q=an:06580140}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Nguyen Tien Zung, “Orbital Linearization of Smooth Completely Integrable Vector Fields”, SIGMA, 13 (2017), 093, 11 pp.  mathnet  crossref
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