In this paper we study the quasi-homogeneous polynomial differential systems and provide an algorithm for obtaining all these systems with a given degree. Using this algorithm we obtain all quasi-homogeneous vector fields of degree 2 and 3.The quasi-homogeneous polynomial differential systems are Liouvillian integrable. In particular, we characterize all the quasi-homogeneous vector fields of degree 2 and 3 having a polynomial, rational or global analytical first integral. © 2013 Elsevier Inc.
|Journal||Journal of Differential Equations|
|Publication status||Published - 15 Nov 2013|
- Analytic first integral
- Polynomial first integral
- Quasi-homogeneous polynomial differential system
- Quasi-homogeneous polynomial vector field
García, B., Llibre, J., & Pérez del Río, J. S. (2013). Planar quasi-homogeneous polynomial differential systems and their integrability. Journal of Differential Equations, 255(10), 3185-3204. https://doi.org/10.1016/j.jde.2013.07.032