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Differential Galois Theory and Lie Symmetries
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Differential Galois Theory and Lie Symmetries
Інший ID:
2010 Mathematics Subject Classification: 12H05; 34M15; 34A26
DOI:10.3842/SIGMA.2015.092
DOI:10.3842/SIGMA.2015.092
Посилання:
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.
Підтримка:
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.
Дата:
2015
Переглядів:
564
Завантажень:
161
Анотація:
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.
