CAJ | 학술논문

本文研究一类(n+1)次多项式系统极限环的存在性及无穷远奇点的类型。根据微分方程几何理论计算焦点量，考虑了系统的中心焦点问题，利用旋转向量场与广义Li′enard系统理论，获得了系统极限环存在的充分条件。同时利用Poincar′e变换，分析了系统无穷远奇点的类型。这些工作突破了已有结论关于系统阶数的局限性，因而具有更广泛的应用范围。
본문연구일류(n+1)차다항식계통겁한배적존재성급무궁원기점적류형。근거미분방정궤하이론계산초점량，고필료계통적중심초점문제，이용선전향량장여엄의Li′enard계통이론，획득료계통겁한배존재적충분조건。동시이용Poincar′e변환，분석료계통무궁원기점적류형。저사공작돌파료이유결론관우계통계수적국한성，인이구유경엄범적응용범위。
In this paper, we investigate the existence of limit cycles and the types of critical points at infinity for a class of (n+1)-th polynomial systems. According to the geo-metrical theory of differential equation, by computing the focal values, the problem of center and focus is considered. By applying the theories of rotated vector field and generalized Li′enard system, a series of su?cient conditions are developed to guarantee the existence of limit cycles, and the types of critical points at infinity are also discussed by Poincar′e transformation. These works improve the results of the differential system. Therefore, it has wide range of application for accompany systems.