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The time evolution governed by Hamilton's equations is an example of continuous canonical transformation. The infinitesimal generator of this transformation is the Hamiltonian itself.
The change in a function \(F(q,p)\) in time \(\Delta t\) is given by
\begin{eqnarray} \Delta F &=&F(q+\Delta q, p + \Delta p) - F(q,p)\\ &=& \{F, H\}_\text{PB} \Delta t. \end{eqnarray}
The above equation showa that the time evolution is a canonical transformation with the Hamiltonian as the generator of infinitesimal time translation.
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