Abstract
In this paper we find necessary and suficient conditions in or- der that a planar quasi{homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi{ homogeneous polynomial differential system can be transformed into a differen- tial system of the form u· = uf(v), v· = g(v) with f(v) and g(v) polynomials, and vice versa.
Original language | English |
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Pages (from-to) | 4531-4547 |
Journal | Discrete and Continuous Dynamical Systems |
Volume | 33 |
Issue number | 10 |
DOIs | |
Publication status | Published - 1 Oct 2013 |
Keywords
- Integrability problem
- Polynomial first integral
- Quasi{homogeneous polynomial differential equations
- Rational first integral