论文标题
二次Lotka-Volterra双中心的摄动理论
Perturbation theory of the quadratic Lotka-Volterra double center
论文作者
论文摘要
我们对Lotka -Volterra二次系统的分叉理论进行了重新审查{eqnarray} x_0：\ left \ {\ oken {aligned} \ dot} \ dot {x} =＆ - y -x y -x^2+y^2+y^2，\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \ \ \ \ \ \ \ \; \ end {Aligned} \ right。 \ end {eqnarray}相对于任意二次变形。系统$ x_0 $具有双中心，此外是等级的。我们表明，变形的系统$ x_0 $最多可以在有限平面上具有两个限制周期，其中可能的分配$（i，j）$，其中$ i+j \ j \ leq2 $。我们的方法基于对与中心相关的分叉函数对的研究，该函数是根据迭代的路径积分表示的。
We revisit the bifurcation theory of the Lotka-Volterra quadratic system \begin{eqnarray} X_0 :\left\{\begin{aligned} \dot{x}=& - y -x^2+y^2 ,\\ \dot{y}= &\;\;\;\;x - 2xy \end{aligned} \right. \end{eqnarray} with respect to arbitrary quadratic deformations. The system $X_0$ has a double center, which is moreover isochronous. We show that the deformed system $X_0$ can have at most two limit cycles on the finite plane, with possible distribution $(i,j)$, where $i+j\leq2$. Our approach is based on the study of pairs of bifurcation functions associated to the centers, expressed in terms of iterated path integrals of length two.
