Homework Help: Transformations of phase space

1. Mar 26, 2010

Nusc

1. The problem statement, all variables and given/known data
The phase flow is the one-parameter group of transformations of phase space

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

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?

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

2. Relevant equations

3. The attempt at a solution

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