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

F. Manosas, J. Villadelprat

Research output: Contribution to journalArticleResearchpeer-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 languageEnglish
Pages (from-to)1631-1642
JournalProceedings of the American Mathematical Society
Volume136
DOIs
Publication statusPublished - 1 May 2008

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