中文摘要：

研究一类2n＋1次多项式微分自治系统在无穷远点的奇点量、中心条件与极限环问题．通过计算推断与理论证明，得出了该系统在无穷远点奇点量的表达式．在此基础上给了该类系统无穷远点成为中心和成为最高阶细焦点的条件，并构造了这类系统在无穷远点分支出3个极限环的实例．

英文摘要：

In this paper, it is studied that center conditions and bifurcations of limit cycles at infinity for a class of 2n＋ 1 -degree polynomial autonomous differential system. By deducing and computation, singular point values at infinity of the system are given. And then the conditions of infinity to be a center and to be the most high-order weak focus are obtained respectively. Finally, an example of polynomial system of 2n＋ 1-degree with three limit cycles at infinity is given.