On the reversible quadratic centers with monotonic period function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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On the reversible quadratic centers with monotonic period function

Authors:	J Villadelprat

Institution:	Departament d'Enginyeria Informàtica i Matemàtiques, ETSE, Universitat Rovira i Virgili, 43007 Tarragona, Spain

Abstract:	This paper is devoted to studying 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 $\begin{displaymath} \left\{ \begin{array}{l} \dot x=-y+xy, 1pt] \dot y=x+Dx^2+Fy^2. \end{array}\right. \end{displaymath}$ We determine several regions in the parameter plane for which the corresponding center has a monotonic period function. To this end we first show that any of these systems can be brought by means of a coordinate transformation to a potential system. Then we apply a monotonicity criterium of R. Schaaf.

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