Abstract
In the smooth (C∞) 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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Jiang, K. Local normal forms of smooth weakly hyperbolic integrable systems. Regul. Chaot. Dyn. 21, 18–23 (2016). https://doi.org/10.1134/S1560354716010020
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DOI: https://doi.org/10.1134/S1560354716010020