Let be $w_0 \in \mathbb{R}^3$ and $X: S^2 \rightarrow TS^2$ the vector field on $S^2$defined by: $$X(v)=w_0- \langle v, w_0 \rangle v.$$ ($\langle.,. \rangle$ is the standard dot product)
How can I describe the local flux of $X$?
I have written the components of $X$ and then I have found the Cauchy problem in order to find the integral curves. The problem is that the differential equations that I' ve found are difficult to resolve.
Is there another way to find the local flux?
Thanks for the help.