TY - JOUR
T1 - Analytic integrability of a class of planar polynomial differential systems
AU - Llibre, Jaume
AU - Valls, Claudia
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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.
AB - 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.
KW - Analytic first integrals
KW - Planar polynomial systems
KW - Pseudo-meromorphic first integrals
KW - Quasi-homogeneous polynomial differential systems
U2 - 10.3934/dcdsb.2015.20.2657
DO - 10.3934/dcdsb.2015.20.2657
M3 - Article
SN - 1531-3492
VL - 20
SP - 2657
EP - 2661
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
IS - 8
ER -