Liénard and Riccati differential equations related via Lie Algebras

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September 2008, 10(2&3, September): 485-494. doi: 10.3934/dcdsb.2008.10.485

Liénard and Riccati differential equations related via Lie Algebras

Isaac A. García ^1, , Jaume Giné ^1, and Jaume Llibre ^2,

1.	Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69, 25001 Lleida, Spain, Spain
2.	Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona

Received September 2006 Revised June 2007 Published June 2008

Abstract
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In this work we study the Liénard systems that can be transformed into Riccati differential equations, using changes of variables more general than the ones used by the classical Lie theory.

Keywords: Lie algebra, integrability., Liénard system, Riccati differential equation.

Mathematics Subject Classification: Primary 34C05, 34C14, 34A05, 22E0.

Citation: Isaac A. García, Jaume Giné, Jaume Llibre. Liénard and Riccati differential equations related via Lie Algebras. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 485-494. doi: 10.3934/dcdsb.2008.10.485

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