## On the reversible quadratic centers with monotonic period function

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- by J. Villadelprat PDF
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**135**(2007), 2555-2565 Request permission

## 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.## References

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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: https://doi.org/10.1090/S0002-9939-07-08749-7
- MathSciNet review: 2302576