TY - JOUR
T1 - On the number of limit cycles surrounding a unique singular point for polynomial differential systems of arbitrary degree
AU - García, Belén
AU - Llibre, Jaume
AU - Pérez del Río, Jesús S.
PY - 2008/12/15
Y1 - 2008/12/15
N2 - We study the number of limit cycles that bifurcate from the periodic orbits of the center over(x, ̇) = - y R (x, y), over(y, ̇) = x R (x, y) where R is a convenient polynomial of degree 2, when we perturb it inside the class of all polynomial differential systems of degree n. We use averaging theory for computing this number. As a consequence of our study we provide the biggest number of limit cycles surrounding a unique singular point in terms of the degree of the system, known up to now. © 2007 Elsevier Ltd. All rights reserved.
AB - We study the number of limit cycles that bifurcate from the periodic orbits of the center over(x, ̇) = - y R (x, y), over(y, ̇) = x R (x, y) where R is a convenient polynomial of degree 2, when we perturb it inside the class of all polynomial differential systems of degree n. We use averaging theory for computing this number. As a consequence of our study we provide the biggest number of limit cycles surrounding a unique singular point in terms of the degree of the system, known up to now. © 2007 Elsevier Ltd. All rights reserved.
KW - Averaging theory
KW - Bifurcation from a center
KW - Limit cycle
U2 - https://doi.org/10.1016/j.na.2007.11.004
DO - https://doi.org/10.1016/j.na.2007.11.004
M3 - Article
VL - 69
SP - 4461
EP - 4469
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
ER -