二阶多项式系统固定奇点附近解的解析展开

ANALYTIC EXPANSION OF SOLUTION PASSING SINGULAR POINT OF SECOND ORDER POLYNOMIAL SYSTEM

研究二阶多项式系统所确定的通过固定奇点的解．利用牛顿图法研究了这种解在固定奇点处的幂级数展开式，给出有无穷多个解通过固定奇点的判据，并在只有有限个解通过固定奇点的情况下，给出了过固定奇点的解个数的上界．

Solutions passing the singular points of second order polynomial system are studied. Expand the solutions near the singular point by using the method presented by Newton while studying algebraic function. Through the method, a criterion of whether there are infinite solutions passing the singular point is given, and while not the case) an upper-bound of such solutions is also given.