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

$\displaystyle g^t{\bf{p}}(0),{\bf{q}}(0))\longmapsto({\bf{p}}(t),{\ bf{q}}(t)) $,

where $\displaystyle {\bf{p}}(t)$ and $\displaystyle {\bf{q}}(t)$ are solutions of the Hamilton's system of equations corresponding to initial condition $\displaystyle {\bf{p}}(0) $and $\displaystyle {\bf{q}}(0)$.

Show that $\displaystyle \{g^t\}$ is a group.

Can anyone help me prove the composition?

$\displaystyle g^t\circ g^s=g^{t+s}$