TY - JOUR
T1 - Global centers of a class of cubic polynomial differential systems
AU - Llibre, Jaume
AU - Rondón, Gabriel
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2024.
PY - 2024/4/25
Y1 - 2024/4/25
N2 - A difficult classical problem in the qualitative theory of differential systems in the plane R is the center-focus problem, i.e. to distinguish between a focus and a center. Another difficult problem is to distinguish inside a family of centers the ones which are global. A global center is a center p such that R\{p} is filled with periodic orbits. In this paper we classify the global centers of the family of real polynomial differential systems of degree 3 that in complex notation write (Formula presented.) where w = x + iy and A ∈ C for k = 3, 4, 5, 6.
AB - A difficult classical problem in the qualitative theory of differential systems in the plane R is the center-focus problem, i.e. to distinguish between a focus and a center. Another difficult problem is to distinguish inside a family of centers the ones which are global. A global center is a center p such that R\{p} is filled with periodic orbits. In this paper we classify the global centers of the family of real polynomial differential systems of degree 3 that in complex notation write (Formula presented.) where w = x + iy and A ∈ C for k = 3, 4, 5, 6.
KW - 34C05
KW - Global centers
KW - Polynomial differential equations
KW - Vertical blow-up
UR - http://www.scopus.com/inward/record.url?scp=85191489726&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/7b648938-6947-3cf4-ba35-c511b6d6df81/
U2 - 10.1007/s12215-024-01034-2
DO - 10.1007/s12215-024-01034-2
M3 - Article
SN - 0009-725X
VL - 73
SP - 2141
EP - 2160
JO - Rendiconti del Circolo Matematico di Palermo
JF - Rendiconti del Circolo Matematico di Palermo
IS - 5
ER -