Smooth flow
= Smooth flow
{title2=$\phi_t$}
A smooth flow is a smooth one-parameter family of diffeomorphisms satisfying $\phi_0=\mathrm{id}$ and $\phi_{t+s}=\phi_t\circ\phi_s$. Its generating vector field is $F(x)=\partial_t\phi_t(x)|_{t=0}$. On a <closed manifold>, every smooth vector field has a flow defined for all real times.