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Kai Jiang

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


Jiang K.
Local Normal Forms of Smooth Weakly Hyperbolic Integrable Systems
2016, vol. 21, no. 1, pp.  18-23
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
Citation: Jiang K.,  Local Normal Forms of Smooth Weakly Hyperbolic Integrable Systems, Regular and Chaotic Dynamics, 2016, vol. 21, no. 1, pp. 18-23

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