We consider polynomial differential systems in the plane with Liouvillian first integrals. It is shown that all such systems have Darbouxian integrating factors, and that the search for suchâ€¦ (More)

Combining implicit polynomials and algebraic invariants for representing and recognizing complicated objects proves to be a powerful technique. In this paper, we explore the findings of the classicalâ€¦ (More)

In this paper we consider complex differential systems in the plane, which are linearizable in the neighborhood of a nondegenerate centre. We find necessary and sufficient conditions forâ€¦ (More)

We give a class of quadratic systems without rational first integral which contains irreducible algebraic solutions of arbitrarily high degree. The construction gives a negative answer to aâ€¦ (More)

with Î» a non negative number. Our aim is to understand the mechanisms which lead to the origin being linearizable, integrable or normalizable. In the case of integrability and linearizability, thereâ€¦ (More)

We investigate the local integrability and linearizability of three dimensional Lotka-Volterra equations at the origin. Necessary and sufficient conditions for both integrability and linearizabilityâ€¦ (More)

In this paper we study the necessary and sufficient condition under which an orbitally normalizable vector field of saddle or saddle-node type in C is analytically conjugate to its formal normal formâ€¦ (More)

The Darboux theory of integrability for planar polynomial differential equations is a classical field, with connections to Lie symmetries, differential algebra and other areas of mathematics. In theâ€¦ (More)

In this paper we describe the moduli space of germs of generic families of analytic diffeomorphisms which unfold a parabolic fixed point of codimension 1. In [11] (and also [15]), it was shown thatâ€¦ (More)

The benzaldehyde di-n-butylacetal has been synthesized and its reactions with acid chlorides, viz., acetylchloride, benzoylchloride, benzylchloride, perchloricacid, sodiumperchlorate,â€¦ (More)