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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

Isaac A. García 1, and  Jaume Giné 1,

1. 

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

Received  January 2003 Revised  July 2003 Published  January 2004

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 and Continuous Dynamical Systems, 2004, 10 (3) : 755-768. doi: 10.3934/dcds.2004.10.755
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