TY - JOUR
T1 - The bifurcation set of the period function of the dehomogenized loud's centers is bounded
AU - Manosas, F.
AU - Villadelprat, J.
PY - 2008/5/1
Y1 - 2008/5/1
N2 - This paper is concerned with the behaviour of the period function of the quadratic reversible centers. In this context the interesting stratum is the family of the so-called Loud's dehomogenized systems, namely { x = -y + xyy = x + Dx2 + Fy2.In this paper we show that the bifurcation set of the period function of these centers is contained in the rectangle K = (-7, 2) X (0, 4). More concretely, we prove that if (D, F) ∉ K, then the period function of the center is monotoni- cally increasing. © 2008 American Mathematical Society.
AB - This paper is concerned with the behaviour of the period function of the quadratic reversible centers. In this context the interesting stratum is the family of the so-called Loud's dehomogenized systems, namely { x = -y + xyy = x + Dx2 + Fy2.In this paper we show that the bifurcation set of the period function of these centers is contained in the rectangle K = (-7, 2) X (0, 4). More concretely, we prove that if (D, F) ∉ K, then the period function of the center is monotoni- cally increasing. © 2008 American Mathematical Society.
U2 - 10.1090/S0002-9939-08-09131-4
DO - 10.1090/S0002-9939-08-09131-4
M3 - Article
SN - 0002-9939
VL - 136
SP - 1631
EP - 1642
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
ER -