The bifurcation set of the period function of the dehomogenized Loud’s centers is bounded

Mañosas, F.; Villadelprat, J.

doi:10.1090/S0002-9939-08-09131-4

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

Proc. Amer. Math. Soc. 136 (2008), 1631-1642 Request permission

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.

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