Recent Applications of the Theory of Lie Systems in Ermakov Systems

José F. Cariñena ; Javier de Lucas ; Manuel F. Rañada

Symmetry, integrability and geometry: methods and applications, Tome 4 (2008)

Résumé

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.

Détail

Keywords: superposition rule; Pinney equation; Ermakov systems.

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