My Math Forum Composition

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 March 27th, 2010, 05:14 PM #1 Newbie   Joined: Mar 2009 Posts: 8 Thanks: 0 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))" />, 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?
 June 24th, 2010, 08:39 AM #2 Member   Joined: Jun 2010 Posts: 80 Thanks: 0 Re: Composition Hallo, nice to meet you. I'm new in here. I think we could prove composition by the fact that the evolution of the system is uniquely determined by the initial conditions, hence applying gt1 on gt2 is the same as to take (q(t1),p(t1)) as initial condition. See you.

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