TY - JOUR
T1 - Polynomial differential systems with even degree have no global centers
AU - Llibre, Jaume
AU - Valls, Claudia
N1 - Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/11/1
Y1 - 2021/11/1
N2 - Let x˙=P(x,y), y˙=Q(x,y) be a differential system with P and Q real polynomials, and let d=max{degP,degQ}. A singular point p of this differential system is a global center if R2∖{p} is filled with periodic orbits. We prove that if d is even then the polynomial differential systems have no global centers.
AB - Let x˙=P(x,y), y˙=Q(x,y) be a differential system with P and Q real polynomials, and let d=max{degP,degQ}. A singular point p of this differential system is a global center if R2∖{p} is filled with periodic orbits. We prove that if d is even then the polynomial differential systems have no global centers.
KW - Global centers
KW - Poincaré compactification
KW - Polynomial differential system
UR - https://www.scopus.com/pages/publications/85105529945
U2 - 10.1016/j.jmaa.2021.125281
DO - 10.1016/j.jmaa.2021.125281
M3 - Article
AN - SCOPUS:85105529945
SN - 0022-247X
VL - 503
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
M1 - 125281
ER -