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Let [itex] V(x) [/itex] a vector field on a manifold ([itex] R^2 [/itex] in my case), i am looking for a condition on [itex] V(x) [/itex] for which the function [itex] x^µ \rightarrow x^µ + V^µ(x) [/itex] is a diffeomorphism. I read some document speaking about the flow, integral curve for ODE solving but i fail to find a generic condition to avoid V to send two point on the same coordinate. I think about the generator of the diffeomorphism group but it's only defined infinitesimaly.

Thanks

Clément