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

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

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Bibliographic databases:

MSC: 37C05, 37C10, 37C25, 37D05, 37D10, 37J60
Accepted:13.08.2015
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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 \mathnet{http://mi.mathnet.ru/rcd65} \crossref{https://doi.org/10.1134/S1560354716010020} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3457074} \zmath{https://zbmath.org/?q=an:06580140} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000373028300002} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84957591231} 

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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.