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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)
We follow Bogoyavlensky's approach to deal with Bianchi class B cosmological models. We characterize the analytic integrability of such systems.
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)