Differential Galois Theory and Lie Symmetries
We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetries can be seen as solutions of a hierarchy of linear differential systems. We show that the existence of rational symmet...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2015 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2015
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147127 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Differential Galois Theory and Lie Symmetries / D. Blázquez-Sanz, J.J. Morales-Ruiz, Jacques-Arthur Weil // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 22 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862537113310855168 |
|---|---|
| author | Blázquez-Sanz, D. Morales-Ruiz, J.J. Jacques-Arthur Weil |
| author_facet | Blázquez-Sanz, D. Morales-Ruiz, J.J. Jacques-Arthur Weil |
| citation_txt | Differential Galois Theory and Lie Symmetries / D. Blázquez-Sanz, J.J. Morales-Ruiz, Jacques-Arthur Weil // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetries can be seen as solutions of a hierarchy of linear differential systems. We show that the existence of rational symmetries constrains the differential Galois group in the system in a way that depends of the Maclaurin series of the symmetry along the zero solution.
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| first_indexed | 2025-11-24T11:44:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147127 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T11:44:39Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Blázquez-Sanz, D. Morales-Ruiz, J.J. Jacques-Arthur Weil 2019-02-13T17:09:53Z 2019-02-13T17:09:53Z 2015 Differential Galois Theory and Lie Symmetries / D. Blázquez-Sanz, J.J. Morales-Ruiz, Jacques-Arthur Weil // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 12H05; 34M15; 34A26 DOI:10.3842/SIGMA.2015.092 https://nasplib.isofts.kiev.ua/handle/123456789/147127 We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetries can be seen as solutions of a hierarchy of linear differential systems. We show that the existence of rational symmetries constrains the differential Galois group in the system in a way that depends of the Maclaurin series of the symmetry along the zero solution. This paper is a contribution to the Special Issue on Algebraic Methods in Dynamical Systems. The full
 collection is available at http://www.emis.de/journals/SIGMA/AMDS2014.html.
 The authors thank their colleagues for interesting discussions that encouraged them to write this
 paper, especially those attending the meeting Algebraic Methods in Dynamical Systems 2014.
 David Bl´azquez-Sanz acknowledges Universidad Nacional de Colombia for supporting his research
 through project ref. HERMES-27984. Juan J. Morales-Ruiz research has been also
 partially supported by the Spanish MINECO-FEDER Grant MTM2012-31714. We thank the
 anonymous referees for their remarks and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Differential Galois Theory and Lie Symmetries Article published earlier |
| spellingShingle | Differential Galois Theory and Lie Symmetries Blázquez-Sanz, D. Morales-Ruiz, J.J. Jacques-Arthur Weil |
| title | Differential Galois Theory and Lie Symmetries |
| title_full | Differential Galois Theory and Lie Symmetries |
| title_fullStr | Differential Galois Theory and Lie Symmetries |
| title_full_unstemmed | Differential Galois Theory and Lie Symmetries |
| title_short | Differential Galois Theory and Lie Symmetries |
| title_sort | differential galois theory and lie symmetries |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147127 |
| work_keys_str_mv | AT blazquezsanzd differentialgaloistheoryandliesymmetries AT moralesruizjj differentialgaloistheoryandliesymmetries AT jacquesarthurweil differentialgaloistheoryandliesymmetries |