The bifurcation set of the period function of the dehomogenized Loud's centers is bounded期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	F Mañ osas J Villadelprat

Institution:	Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain J. Villadelprat ; Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain

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 $\begin{displaymath} \left\{ \begin{array}{l} \dot x=-y+xy, 1pt] \dot y=x+Dx^2+Fy^2. \end{array}\right. \end{displaymath}$ In this paper we show that the bifurcation set of the period function of these centers is contained in the rectangle $K=(-7,2)\times(0,4).$ More concretely, we prove that if $(D,F)\notin K$ , then the period function of the center is monotonically increasing.

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