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flow generated by vector field


Is there a way to compute the *flow* of a vector field
(used in the theory of Lie derivatives), that satisfies

d/dt sigma_mue(t,x0)= X_mue (sigma(t,x0))

example: sigma(t,(x,y))= (x Cos[t] - y Sin[t], x Sin[t] + y Cos[t])

is the flow generated by the vector field (-y @/@x, x @/@y)

I tried   DSolve without success.

Thanks,

Alexander Unzicker

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