论文标题
在$（\ Mathbb {s}^2）上的线性向量字段的限制循环
Limit cycles of linear vector fields on $(\mathbb{S}^2)^m \times \mathbb{R}^n$
论文作者
论文摘要
众所周知，在$ \ mathbb {r}^n $中定义的线性向量字段不能具有限制周期，但是对于其他歧管中定义的线性向量字段并非如此。我们研究了从形式的$（\ Mathbb {s}^2）^M \ times \ times \ m athbb {r}^n $的形式的歧管上的限制周期的存在。该研究是使用平均理论完成的。我们还提出了一个开放的问题，即$（\ mathbb {s}^2）^m \ times \ times \ mathbb {r}^n $在$（\ mathbb {s}^2）上的线性向量字段的最大限制数量。
It is well known that linear vector fields defined in $\mathbb{R}^n$ can not have limit cycles, but this is not the case for linear vector fields defined in other manifolds. We study the existence of limit cycles bifurcating from a continuum of periodic orbits of linear vector fields on manifolds of the form $(\mathbb{S}^2)^m \times \mathbb{R}^n$ when such vector fields are perturbed inside the class of all linear vector fields. The study is done using the averaging theory. We also present an open problem concerning the maximum number of limit cycles of linear vector fields on $(\mathbb{S}^2)^m \times \mathbb{R}^n$.
