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## Main Question or Discussion Point

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

[tex]g^t:({\bf{p}(0),{\bf{q}(0))\longmapsto({\bf{p}(t),{\bf{q}(t)) [/tex],

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

Show that [tex]\{g^t\}[/tex] is a group.

Can anyone help me prove the composition?

[tex]g^t\circ g^s=g^{t+s}[/tex]

[tex]g^t:({\bf{p}(0),{\bf{q}(0))\longmapsto({\bf{p}(t),{\bf{q}(t)) [/tex],

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

Show that [tex]\{g^t\}[/tex] is a group.

Can anyone help me prove the composition?

[tex]g^t\circ g^s=g^{t+s}[/tex]