Abstract
ABSTRACTThe quartic–linear polynomial differential systems having at least one finite singularity are affine equivalent to systems of the formwhere P and Q are coprime, Pi are homogeneous polynomials of degree i and (otherwise it is cubic–linear) and Q(x, y) is either x or y. In this paper, we classify all the quartic–linear systems with Q(x, y) = y which have a global C∞ first integral. We use the local characterization of first integrals, partition of unity in and smoothness of first integrals in canonical regions.
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