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On the reversible quadratic centers with monotonic period function

Author: J. Villadelprat
Journal: Proc. Amer. Math. Soc. 135 (2007), 2555-2565
MSC (2000): Primary 34C07, 34C25
Published electronically: 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 \[ \left \{ \begin {array}{l} \dot x=-y+xy, [1pt] \dot y=x+Dx^2+Fy^2. \end {array} \right . \] 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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J. Villadelprat
Affiliation: Departament d’Enginyeria Informàtica i Matemàtiques, ETSE, Universitat Rovira i Virgili, 43007 Tarragona, Spain

Received by editor(s): March 13, 2006
Received by editor(s) in revised form: April 11, 2006
Published electronically: February 6, 2007
Additional Notes: The author was partially supported by CONACIT through grant 2001SGR-00173 and by DGES through grant MTM2005-06098-C02-1.
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.