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Journals and Conferences
In this paper we study the normal forms of polynomial systems having a set of given generic invariant algebraic curves. PACS numbers: 02.30.Ik, 02.10.De
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… (More)
Polynomial vector fields which admit a prescribed Darboux integrating factor are quite well-understood when the geometry of the underlying curve is nondegenerate. In the general setting morphisms of the affine plane may remove degeneracies of the curve, and thus allow more structural insight. In the present paper we establish some properties of integrating… (More)
Antoni Ferragut, a) Jaume Llibre, b) and Chara Pantazi c) Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, ETSEIB, Av. Diagonal, 647, 08028, Barcelona, Catalonia, Spain Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193 Bellaterra, Barcelona, Catalonia, Spain Departament de Matemàtica Aplicada I,… (More)
We study the maximum number of limit cycles that can bifurcate from a degenerate center of a cubic homogeneous polynomial differential system. Using the averaging method of second order and perturbing inside the class of all cubic polynomial differential systems we prove that at most three limit cycles can bifurcate from the degenerate center. As far as we… (More)
We follow Bogoyavlensky's approach to deal with Bianchi class B cosmological models. We characterize the analytic integrability of such systems.
We complete the study of the analytic integrability of the Class A of Bianchi cosmological models with k = 1, characterizing the analytic first integrals of the Bianchi types VI0 and VIII0.
In this paper we study the Darboux transformations of planar vector fields of Schrödinger type. Using the isogaloisian property of Darboux transformation we prove the “invariance” of the objects of the “Darboux theory of integrability”. In particular, we also show how the shape invariance property of the potential is important in order to preserve the… (More)