Characteristic functional structure of infinitesimal symmetry transformations of Birkhoffian systems

In this paper, it is shown that infinitesimal symmetry transformations of Birkhoffian systems have a characteristic functional structure, which is formulated by means of an auxiliary symmetry transformation function Z_\mu(t,a) (introduced by the relation \xi_\mu(t,a)=Z_\mu(t,a)+\dota^\mu\xi_0 (t, a)) and is manifestly dependent upon the constants of motion of the system. At the end of the paper, an example is given to illustrate the application of the results.