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Thread: Composition

  1. #1
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    Question Composition

    The phase flow is the one-parameter 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?

    $\displaystyle g^t\circ g^s=g^{t+s}$
    Last edited by Opalg; Mar 28th 2010 at 09:44 AM. Reason: fixed LaTeX
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