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Un-Reduction of Systems of Second-Order Ordinary Differential Equations
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Un-Reduction of Systems of Second-Order Ordinary Differential Equations
Інший ID:
2010 Mathematics Subject Classification: 34A26; 37J15; 70H33; 70G65
DOI:10.3842/SIGMA.2016.115
DOI:10.3842/SIGMA.2016.115
Посилання:
Un-Reduction of Systems of Second-Order Ordinary Differential Equations / E. García-Toraño Andrés, T. Mestdag // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 19 назв. — англ.
Підтримка:
EGTA thanks the CONICET for financial support through a Postdoctoral Grant. TM is a visiting
professor at Ghent University: he is grateful to the Department of Mathematics for its
hospitality.
Дата:
2016
Переглядів:
593
Завантажень:
237
Анотація:
In this paper we consider an alternative approach to ''un-reduction''. This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential equations (SODEs), one may associate to the first system a (what we have called) ''primary un-reduced SODE'', and we explain how all other un-reduced SODEs relate to it. We give examples that show that the considered procedure exceeds the realm of Lagrangian systems and that relate our results to those in the literature.
