
Composition
The phase flow is the oneparameter 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?
$\displaystyle g^t\circ g^s=g^{t+s}$