This article is cited in 2 papers

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.

MSC: 37C05, 37C10, 37C25, 37D05, 37D10, 37J60

Received: 02.04.2015
Accepted: 13.08.2015

Language: English

DOI: 10.1134/S1560354716010020

Bibliographic databases:

• 
• 
• 
•