The phase flow is the one-parameter group of transformations of phase space

{\bf{p}}(0),{\bf{q}}(0))\longmapsto({\bf{p}}(t),{\ bf{q}}(t)) " alt="g^t{\bf{p}}(0),{\bf{q}}(0))\longmapsto({\bf{p}}(t),{\ bf{q}}(t)) " />,

where and are solutions of the Hamilton's system of equations corresponding to initial condition and .

Show that is a group.

Can anyone help me prove the composition?