One-parameter groups

Julien Santini · science forum addict Joined: 06 May 2005 Posts: 60

Hello,

Considering a one-parameter group f: M x R -> M, where M is a
differentiable manifold; is it true that its infinitesimal generator,
namely the vector vield which associates to x the tangent vector at
point x given by the curve t->f(x,t), is a C^(+oo) vector field ?

I read that thing in Sternberg's course (5.3 p.380, Advanced Calculus),
but it seems to me that since f is supposed to be only differentiable,
the infinitesimal generator of f should be only differentiable ...
Maybe there is some inductive stuff that guarantees C^(+oo), but I
can't see it ...

Thanks for any help,

--
Julien Santini

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