Non-algebraic invariant curves for polynomial planar vector fields

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July 2004, 10(3): 755-768. doi: 10.3934/dcds.2004.10.755

Non-algebraic invariant curves for polynomial planar vector fields

1.	Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69. 25001. Lleida., Spain, Spain

Received January 2003 Revised July 2003 Published January 2004

Abstract
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In this paper we give, as far as we know, the first method to detect non-algebraic invariant curves for polynomial planar vector fields. This approach is based on the existence of a generalized cofactor for such curves. As an application of this algorithmic method we give some Lotka-Volterra systems with non-algebraic invariant curves.

Keywords: Nonlinear differential equations, Liouvillian and non-Liouvillian ﬁrst integral., non-algebraic invariant curves.

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

Citation: Isaac A. García, Jaume Giné. Non-algebraic invariant curves for polynomial planar vector fields. Discrete & Continuous Dynamical Systems - A, 2004, 10 (3) : 755-768. doi: 10.3934/dcds.2004.10.755

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