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Polynomial differential systems having a given Darbouxian first integral
Llibre Saló, Jaume; Pantazi, Chara
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
The Darbouxian theory of integrability allows to determine when a polynomial differential system in C2 has a first integral of the kind f λ1 1 ···f λp p exp(g/h) where fi , g and h are polynomials in C[x, y], and λi ∈ C 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 C2 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.
Peer Reviewed
Differential equations
Polynomial differential system
First integral
Darbouxian function
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Artículo
Elsevier
         

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