Lie derivative at a zero of its generator
= Lie derivative at a zero of its generator
{c}
The <tensor Lie derivative> need not vanish at a point where its generating <vector field> vanishes. For $X=x\partial_x$, the local flow fixes zero but its differential rescales tangent vectors; $\mathcal L_Xdx=dx$ even there. Straightening coordinates exist only at nonzero generator points. The flow definition remains valid at zeros and includes derivatives of the generator acting on tensor slots.