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Orbital Linearization of Smooth Completely Integrable Vector Fields
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Orbital Linearization of Smooth Completely Integrable Vector Fields
Інший ID:
2010 Mathematics Subject Classification: 37G05; 58K50; 37J35
DOI:10.3842/SIGMA.2017.093
DOI:10.3842/SIGMA.2017.093
Посилання:
Orbital Linearization of Smooth Completely Integrable Vector Fields / N.T. Zung // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 15 назв. — англ.
Підтримка:
The first version of this manuscript was available since 2012 as an unpublished preprint (see
arXiv:1204.5701v1). It was then revised and submitted during the author’s stay at the School
of Mathematical Sciences, Shanghai Jiao Tong University, as a visiting professor in 2017. He
would like to thank Shanghai Jiao Tong University, and especially Tudor Ratiu, Jianshu Li, and
Jie Hu for the invitation, hospitality and excellent working conditions.
The authors would also like to thank the referees of this paper for many pertinent remarks
which helped improve the presentation of the paper.
Дата:
2017
Переглядів:
426
Завантажень:
221
Анотація:
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.
