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Infinitesimal Generator of a Group Action
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The answer per the hint is given as follows. We have $\theta(t; x, y) = (xe^{2t}, ye^{-3t})$. On inspection, we see that it is an action, as $\theta(0; x, y) = (x, y)$ and $\theta(t+s; x, y) = \theta(...

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