José F. Cariñena, Javier de Lucas, Manuel F. Rañada, “Recent Applications of the Theory of Lie Systems in Ermakov Systems”, SIGMA, 2008, Volume 4,031, 18 pp.

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Recent Applications of the Theory of Lie Systems in Ermakov Systems

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

Department of Theoretical Physics, University of Zaragoza, 50.009 Zaragoza, Spain

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.

Keywords: superposition rule; Pinney equation; Ermakov systems.

MSC: 34A26; 34A05

Received: November 2, 2007; in final form February 4, 2008; Published online March 12, 2008

Language: English

DOI: 10.3842/SIGMA.2008.031