Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities
Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities
复制标题
DOI：
10.3934/dcdsb.2016.21.121
复制
发表时间：
2015-11
影响因子：
1.2
通讯作者：
Jackson Itikawa;J. Llibre
中科院分区：
文献类型：
--
作者：
Jackson Itikawa;J. Llibre
我们对微分系统$点{x}=-y+xf(x，y)，$$点{y}=x+yf(x，y)$的Poincare圆盘上的全局相图进行了分类，其中$f(x，y)$是3次齐次多项式。这些系统在原点有一个一致的等时中心。本文结合文[9]的结果，完成了所有四次多项式微分系统在原点具有一致等时中心的Poincare圆盘上的全局相图的分类。
We classify the global phase portraits in the Poincare disc of the differential systems $\dot{x}=-y+xf(x,y),$ $\dot{y}=x+yf(x,y)$, where $f(x,y)$ is a homogeneous polynomial of degree 3. These systems have a uniform isochronous center at the origin. This paper together with the results presented in [9] completes the classification of the global phase portraits in the Poincare disc of all quartic polynomial differential systems with a uniform isochronous center at the origin.