So there is a nice notation for a one-parameter group of transformations $\Phi_t$ corresponding to its infinitesimal generator $\boldsymbol X$:
$$\Phi_t = \exp \left(t \boldsymbol X \right)$$
But what is a common notation then for pull-back ${\Phi_t}^*$ and pushforward ${\Phi_t}_*$ when written via exponent?