Polynomial differential systems having a given Darbouxian first integral |
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Authors: | Jaume Llibre Chara Pantazi |
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Institution: | Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain |
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Abstract: | The Darbouxian theory of integrability allows to determine when a polynomial differential system in has a first integral of the kind f1λ1?fpλpexp(g/h) where fi, g and h are polynomials in , and for i=1,…,p. The functions of this form are called Darbouxian functions. Here, we solve the inverse problem, i.e. we characterize the polynomial vector fields in having a given Darbouxian function as a first integral.On the other hand, using information about the degree of the invariant algebraic curves of a polynomial vector field, we improve the conditions for the existence of an integrating factor in the Darbouxian theory of integrability. |
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Keywords: | 34C05 34A34 34C14 |
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