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One-parameter groups
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Julien Santini
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Joined: 06 May 2005
Posts: 60

PostPosted: Fri Jul 21, 2006 7:52 am    Post subject: One-parameter groups Reply with quote


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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