Recent Applications of the Theory of Lie Systems in Ermakov Systems

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2008
• Main Authors: Cariñena, J.F., de Lucas, J., Rañada, M.F.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149010
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...