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Symmetry, Integrability and Geometry: Methods and Applications, 2008, Volume 4, 031, 18 pp.
DOI: https://doi.org/10.3842/SIGMA.2008.031 (Mi sigma284) 		 
This article is cited in 36 scientific papers (total in 36 papers)

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
Full-text PDF (276 kB) Citations (36)
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DOI: https://doi.org/10.3842/SIGMA.2008.031
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.
Received: November 2, 2007; in final form February 4, 2008; Published online March 12, 2008
Bibliographic databases:
Document Type: Article
MSC: 34A26; 34A05
Language: English
Citation: José F. Cariñena, Javier de Lucas, Manuel F. Rañada, “Recent Applications of the Theory of Lie Systems in Ermakov Systems”, SIGMA, 4 (2008), 031, 18 pp.
Citation in format AMSBIB
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\by Jos{\'e} F.~Cari\~nena, Javier de Lucas, Manuel F.~Ra\~nada
\paper Recent Applications of the Theory of Lie Systems in Ermakov Systems
\jour SIGMA
\yr 2008
\vol 4
\papernumber 031
\totalpages 18
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    • This publication is cited in the following 36 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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