关于由系数矩确定的常微分方程的中心集
On Center Sets of ODEs Determined by Moments of their Coefficients
摘要：
经典的H. Poincaré中心-焦点问题是关于平面多项式向量场的特征，使得它们的所有积分轨迹都是内部包含不动点（{ \em中心}）的闭曲线。这个问题可以归结为一个常微分方程的中心问题，该方程的系数是多项式依赖于域的系数的三角多项式。本文证明了Center-Focus问题的中心集可由该方程系数的矩确定为某些连续函数的零点集。
英文摘要：
The classical H. Poincaré Center-Focus problem asks about the characterization of planar polynomial vector fields such that all their integral trajectories are closed curves whose interiors contain a fixed point, a {\em center}. This problem can be reduced to a center problem for some ordinary differential equation whose coefficients are trigonometric polynomials depending polynomially on the coefficients of the field. In this paper we show that the set of centers in the Center-Focus problem can be determined as the set of zeros of some continuous functions from the moments of coefficients of this equation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
