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Article

Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations

Instituto de Matemática Interdisciplinar and Depto. Geometría y Topología, Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid E-28040, Spain
Academic Editor: Roman M. Cherniha
Symmetry 2016, 8(3), 15; https://doi.org/10.3390/sym8030015
Received: 1 December 2015 / Revised: 24 February 2016 / Accepted: 26 February 2016 / Published: 17 March 2016
(This article belongs to the Special Issue Symmetry and Integrability)
A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebra. In particular, well-known types, such as the Milne-Pinney or Kummer-Schwarz equations, are recovered as special cases of this classification. The analogous problem for systems of second-order differential equations in the real plane is considered for a special case that enlarges the generalized Ermakov systems. View Full-Text
Keywords: Lie systems; Vessiot-Guldberg-Lie algebra; superposition rule; SODE Lie systems Lie systems; Vessiot-Guldberg-Lie algebra; superposition rule; SODE Lie systems
MDPI and ACS Style

Campoamor-Stursberg, R. Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations. Symmetry 2016, 8, 15. https://doi.org/10.3390/sym8030015

AMA Style

Campoamor-Stursberg R. Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations. Symmetry. 2016; 8(3):15. https://doi.org/10.3390/sym8030015

Chicago/Turabian Style

Campoamor-Stursberg, Rutwig. 2016. "Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations" Symmetry 8, no. 3: 15. https://doi.org/10.3390/sym8030015

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