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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the reversible quadratic centers with monotonic period function
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by J. Villadelprat PDF
Proc. Amer. Math. Soc. 135 (2007), 2555-2565 Request permission


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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Additional Information
  • 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
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 2555-2565
  • MSC (2000): Primary 34C07, 34C25
  • DOI:
  • MathSciNet review: 2302576