Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

On the reversible quadratic centers with monotonic period function

Author(s): J. Villadelprat
Journal: Proc. Amer. Math. Soc. 135 (2007), 2555-2565.
MSC (2000): Primary 34C07, 34C25
Posted: February 6, 2007
MathSciNet review: 2302576
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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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