where \(\left\{\bullet,\bullet\right\}\) are the Poisson brackets with respect to the variables \(\left(q,p\right)\). This condition is indeed quite general. However, the only allowed transformation from (\ref{25c}) to the equations (\ref{eq:02a}) is given by \(x=q\), and \(y=e^{-\dot{G}t/2}p\) provided \(G\) is homogeneous of degree zero. This is the case of constant \(g\) that will be addressed below. In this case, (\ref{25c}) are equivalent to (\ref{eq:02a}) only for constant \(g\).