Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 031, 18 pages      arXiv:0803.1824      https://doi.org/10.3842/SIGMA.2008.031
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Recent Applications of the Theory of Lie Systems in Ermakov Systems

José F. Cariñena, Javier de Lucas and Manuel F. Rañada
Department of Theoretical Physics, University of Zaragoza, 50.009 Zaragoza, Spain

Received November 02, 2007, in final form February 04, 2008; Published online March 12, 2008

Abstract
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.

Key words: superposition rule; Pinney equation; Ermakov systems.

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