非线性动力系统多项式首次积分的不存在性

On the Nonexistence of Polynomial First Integrals for Nonlinear Dynamical Systems

给出当f1,…,fn为非线性多项式时,系统dxi(t)/dt=fi(x1(t),…,xn(t))不存在多项式首次积分的1个充分条件:矩阵A的特征根λ1,…,λn不满足任何非共振条件k1λ1+…+knλn=0,k1,…,kn∈Z+,∑from i=1 to n (ki>0).

The paper shows a sufficient condition that the system dxi（t）/dt=fi（x1（t）,…,xn（t）） does not admit polynomial first intergals when f1,…,fn are nonlinear polynomial：the eigenvalues λ1,…,λn of the matrix A are not satisfied with any nonresonant condition k1λ1＋…＋knλn=0,k1,…,kn∈Z^＋,^n∑i=1ki〉0.