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 - https://doi.org/10.1090/S0002-9939-08-09131-4

DO - https://doi.org/10.1090/S0002-9939-08-09131-4

M3 - Article

VL - 136

SP - 1631

EP - 1642

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

ER -