Copyright © DCDSB. 2015. In this paper we find necessary and sufficient conditions in order that the differential systems of the form x. = xf(y), y. = g(y), with f and g polynomials, have a first integral which is analytic in the variable x and meromorphic in the variable y. We also characterize their analytic first integrals in both variables x and y. These polynomial differential systems are important because after a convenient change of variables they contain all quasi-homogeneous polynomial differential systems in ℝ2.
|Journal||Discrete and Continuous Dynamical Systems - Series B|
|Publication status||Published - 1 Jan 2015|
- Analytic first integrals
- Planar polynomial systems
- Pseudo-meromorphic first integrals
- Quasi-homogeneous polynomial differential systems