### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 093, 11 pages      arXiv:1204.5701      https://doi.org/10.3842/SIGMA.2017.093

### Orbital Linearization of Smooth Completely Integrable Vector Fields

Nguyen Tien Zung ab
a) School of Mathematics, Shanghai Jiao Tong University, 800 Dongchuan Road, Minhang District, Shanghai 200240, P.R. China
b) Institut de Mathématiques de Toulouse, UMR5219 CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France

Received July 04, 2017, in final form November 30, 2017; Published online December 12, 2017

Abstract
The main purpose of this paper is to prove the smooth local orbital linearization theorem for smooth vector fields which admit a complete set of first integrals near a nondegenerate singular point. The main tools used in the proof of this theorem are the formal orbital linearization theorem for formal integrable vector fields, the blowing-up method, and the Sternberg-Chen isomorphism theorem for formally-equivalent smooth hyperbolic vector fields.

Key words: integrable system; normal form; linearization; nondegenerate singularity.

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