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Asymptotic Development of an Integral Operator and Boundedness of the Criticality of Potential Centers
Journal of Dynamics and Differential Equations ( IF 1.3 ) Pub Date : 2019-04-22 , DOI: 10.1007/s10884-019-09753-2
David Rojas

We study the asymptotic development at infinity of an integral operator. We use this development to give sufficient conditions to upper bound the number of critical periodic orbits that bifurcate from the outer boundary of the period function of planar potential centers. We apply the main results to two different families: the power-like potential family \(\ddot{x}=x^q-x^p\), \(p,q\in \mathbb {R}\), \(p>q\); and the family of dehomogenized Loud’s centers.

中文翻译:

积分算子的渐近发展与势中心临界度的有界性

我们研究了积分算子无穷大处的渐近发展。我们利用这一发展提供了充分的条件,以使从平面势中心的周期函数的外边界分叉的临界周期轨道的数目上限。我们将主要结果应用于两个不同的族:幂次势族\(\ ddot {x} = x ^ qx ^ p \)\(p,q \ in \ mathbb {R} \)\(p > q \) ; 以及Loud中心去均质的家庭。
更新日期:2019-04-22
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