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Infinitesimal generator of a vector field
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Julien Santini
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Joined: 06 May 2005
Posts: 60

PostPosted: Fri Jul 21, 2006 8:01 am    Post subject: Infinitesimal generator of a vector field Reply with quote

Hello,

Let X be a smooth vector field on a differentiable manifold M. Then
there exists a neighborhood U of M x 0 in M x R and a flow psi: U -> M
having X as its infinitesimal generator.

My question: is it enough to assume X is a C^{2}-vector field ? I would
say yes since it is enough to satisfy the Lipschitz condition ...

As a consequence, can we define the Lie derivative with respect to a
C^{2}-vector field, or do we need to take a smooth vector-field ?

--
Julien Santini
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