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This article is cited in 2 scientific papers (total 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.
Received: 02.04.2015 Accepted: 13.08.2015
Citation:
Kai Jiang, “Local Normal Forms of Smooth Weakly Hyperbolic Integrable Systems”, Regul. Chaotic Dyn., 21:1 (2016), 18–23
Linking options:
https://www.mathnet.ru/eng/rcd65 https://www.mathnet.ru/eng/rcd/v21/i1/p18
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Abstract page: | 207 | References: | 38 |
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