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math-ph2008★ 11 cited
Nonlinear superpositions and Ermakov systems
José F. Cariñena, Javier de Lucas, Manuel F. Rañada
The theory of superposition rules for solutions of a Lie system of first-order differential equations is extended to deal with analogous systems of second-order and the theory is i…
math-ph2008★ 35 cited
Recent Applications of the Theory of Lie Systems in Ermakov Systems
José F. Cariñena, Javier De Lucas, Manuel F. Rañada
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 superp…