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

The bifurcation set of the period function of the dehomogenized Loud’s centers is bounded
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DOI：
10.1090/s0002-9939-08-09131-4
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发表时间：
2008-01
期刊：
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影响因子：
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通讯作者：
F. Mañosas;J. Villadelprat
F. Mañosas;J. Villadelprat
中科院分区：
其他
文献类型：
--
作者：
F. Mañosas;J. Villadelprat

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本文研究二次可逆中心周期函数的性质。在这种情况下，有趣的阶层是所谓的Loud去均匀化系统的家族，即{ x = -y + xy，{y = x+Dx 2 +Fy 2。本文证明了这些中心的周期函数的分支集包含在矩形K =（-7，2）x（0，4）中。更具体地说，我们证明了，如果（D，F）<$K，那么中心的周期函数是单调增加的。
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 { x = -y + xy, {y = x+Dx 2 +Fy 2 . In this paper we show that the bifurcation set of the period function of these centers is contained in the rectangle K = (-7, 2) x (0,4). More concretely, we prove that if (D, F) ∉ K, then the period function of the center is monotonically increasing.