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Recent Applications of the Theory of Lie Systems in Ermakov Systems
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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Recent Applications of the Theory of Lie Systems in Ermakov Systems
Інший ID:
2000 Mathematics Subject Classification: 34A26; 34A05
Посилання:
Recent Applications of the Theory of Lie Systems in Ermakov Systems / J.F. Cariñena, J. de Lucas, M.F. Rañada // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 52 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). Partial financial support by research projects MTM2006-10531 and E24/1 (DGA) are acknowledged. JdL also acknowledge a F.P.U. grant from Ministerio de Educaci´on y Ciencia and a special grant from the Network of Mechanics, Geometry and Control.
Дата:
2008
Переглядів:
405
Завантажень:
154
Анотація:
We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found from this new perspective. We also obtain new results, such as a new superposition rule for the Pinney equation in terms of three solutions of a related Riccati equation.
