# Local Normal Forms of Smooth Weakly Hyperbolic Integrable Systems

*2016, Volume 21, Number 1, pp. 18-23*

Author(s):

**Jiang K.**

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.

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