The bifurcation set of the period function of the dehomogenized Loud’s centers is bounded
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- by F. Mañosas and J. Villadelprat PDF
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Abstract:
This paper is concerned with the behaviour of 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 \[ \left \{ \begin {array}{l} \dot x=-y+xy, [1pt] \dot y=x+Dx^2+Fy^2. \end {array} \right . \] In this paper we show that the bifurcation set of the period function of these centers is contained in the rectangle $K=(-7,2)\!\times \!(0,4).$ More concretely, we prove that if $(D,F)\notin K$, then the period function of the center is monotonically increasing.References
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Additional Information
- F. Mañosas
- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella- terra, Barcelona, Spain
- MR Author ID: 254986
- J. Villadelprat
- Affiliation: Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
- Received by editor(s): October 18, 2006
- Published electronically: January 23, 2008
- Additional Notes: The authors were partially supported by the CONACIT through the grant 2005-SGR-00550 and by the DGES through the grant MTM-2005-06098-C02-1.
- Communicated by: Carmen C. Chicone
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 1631-1642
- MSC (2000): Primary 34C07, 34C23; Secondary 34C25
- DOI: https://doi.org/10.1090/S0002-9939-08-09131-4
- MathSciNet review: 2373592