A general algorithm for the determination ofT j (n) andZ j *(n) in Hori's method for non-canonical systems

A general algorithm for the determination ofT _j ⁽ⁿ⁾ andZ _j ^*(n) is deduced. This algorithm is obtained from the general solution of non-homogeneous linear differential equations with variable coefficients in their matricial form. To do this a new functionX ^*(n) associated withZ ^*(n) is introduced. Then it is possible to calculateZ ^*(n) such that it contains secular or mixed secular terms and soT ⁽ⁿ⁾ is free from these terms.