Orbital Linearization of Smooth Completely Integrable Vector Fields
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 form...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149271 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862551087831056384 |
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| author | Zung, N.T. |
| author_facet | Zung, N.T. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-11-25T20:56:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149271 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T20:56:15Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Zung, N.T. 2019-02-19T19:34:41Z 2019-02-19T19:34:41Z 2017 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. 1815-0659 2010 Mathematics Subject Classification: 37G05; 58K50; 37J35 DOI:10.3842/SIGMA.2017.093 https://nasplib.isofts.kiev.ua/handle/123456789/149271 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Orbital Linearization of Smooth Completely Integrable Vector Fields Article published earlier |
| spellingShingle | Orbital Linearization of Smooth Completely Integrable Vector Fields Zung, N.T. |
| title | Orbital Linearization of Smooth Completely Integrable Vector Fields |
| title_full | Orbital Linearization of Smooth Completely Integrable Vector Fields |
| title_fullStr | Orbital Linearization of Smooth Completely Integrable Vector Fields |
| title_full_unstemmed | Orbital Linearization of Smooth Completely Integrable Vector Fields |
| title_short | Orbital Linearization of Smooth Completely Integrable Vector Fields |
| title_sort | orbital linearization of smooth completely integrable vector fields |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149271 |
| work_keys_str_mv | AT zungnt orbitallinearizationofsmoothcompletelyintegrablevectorfields |