A flow \\(\phi^t\\) on \\(M\\) is called a _global flow_ for the tangent vector field \\(\alpha\\) if for every point \\(s \in M\\), the trajectory function \\(\phi_s(t)\\) is a flow line of \\(\alpha\\).

In other words, the condition is that for all \\(s \in M\\) and \\(t \\in T\\), we have that \\(\phi_s'(t) = \alpha(\phi^t(s))\\).