kroni
- 79
- 10
Hi everybody,
Let V(x) a vector field on a manifold (R^2 in my case), i am looking for a condition on V(x) for which the function x^µ \rightarrow x^µ + V^µ(x) 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
Let V(x) a vector field on a manifold (R^2 in my case), i am looking for a condition on V(x) for which the function x^µ \rightarrow x^µ + V^µ(x) 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