Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems |
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| Authors: | J Chavarriga H Giacomini |
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| Institution: | a Departament de Matemàtica, Universitat de Lleida, Avda, Jaume II, 69. 25001 Lleida, Spain
b Laboratoire de Mathématiques et Physique Théorique, CNRS UMR 6083, Faculté des Sciences et Techniques, Université de Tours, Parc de Grandmont, 37200 Tours, France |
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| Abstract: | This work deals with planar polynomial differential systems  ,  . We give a set of necessary conditions for a system to have an invariant algebraic curve. These conditions are determined from the value of the cofactor at the singular points of the system, once considered in a compact space. We apply these results to show the non-Liouvillian integrability of several families of quadratic systems with an algebraic limit cycle. |
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| Keywords: | 34C05 34C07 34C25 |
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