The bifurcation set of the period function of the dehomogenized loud's centers is bounded

F. Manosas; J. Villadelprat

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

The bifurcation set of the period function of the dehomogenized loud's centers is bounded

F. Manosas, J. Villadelprat

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

15 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1631-1642
Journal	Proceedings of the American Mathematical Society
Volume	136
DOIs	https://doi.org/10.1090/S0002-9939-08-09131-4
Publication status	Published - 1 May 2008

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title = "The bifurcation set of the period function of the dehomogenized loud's centers is bounded",

abstract = "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. {\textcopyright} 2008 American Mathematical Society.",

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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.

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