一类时间可逆系统的可积性

Integrability for a Class of Time-Reversible Systems

对于一类时间可逆解析微分系统,建立了逆积分因子的系数递推公式.利用此递推公式得到其具有指定形式逆积分因子的三个充要条件.为了说明这个结论,对于一个具体的时间可逆三次微分系统,利用系数递推公式直接给出系统的多项式型逆积分因子和有理首次积分.

For a class of time-reversible analytic systems,coefficients′ recurrence formula of inverse integrating factors are obtained,by which three necessary and sufficient conditions for the systems having prescribed inverse integrating factor are reached.To illustrate the results,polynomial inverse intergrating factor and rational first integral of a cubic reversible system are obtained directly by the coefficients＇ recurrence formulae.