CrampinPage64Exercise28

Let V be a vector field on an affine space A generating a flow \phi, let \Psi:A->A be any smooth invertible map with smooth inverse, and let \Phi(t,x)=\Psi(\phi(t,\Psi^{-1}(x))). Show that \Phi is also a flow on A, and that its generator V^\Psi is given by V^\Psi_x=\Psi_*(V_{\Psi^{-1}(x)}).