# Math Help - Composition

1. ## Composition

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

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

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

Can anyone help me prove the composition?

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