论文标题
限制一些平滑和非平滑平面系统家庭的周期
Limit cycles for some families of smooth and non-smooth planar systems
论文作者
论文摘要
在本文中，我们将通过Brouwer学位的平均方法应用于由线性中心给出的一类平面系统，该中心受到连续均匀矢量场的扰动，以研究其极限周期数量的下限。我们的结果可以应用于在集合$σ= \ {xy = 0 \} $上丢失平滑度的模型。我们还将它们应用于希尔伯特（Hilbert）第16个问题的一种变体，其中的目标是按照多项式矢量领域的单一元素数量绑定极限周期的数量，而不是按其学位进行此操作。
In this paper, we apply the averaging method via Brouwer degree in a class of planar systems given by a linear center perturbed by a sum of continuous homogeneous vector fields, to study lower bounds for their number of limit cycles. Our results can be applied to models where the smoothness is lost on the set $Σ=\{xy=0\}$. We also apply them to present a variant of Hilbert 16th problem, where the goal is to bound the number of limit cycles in terms of the number of monomials of a family of polynomial vector fields, instead of doing this in terms of their degrees.
