Time derivatives of pullbacks and push forwards along smooth curves of
diffeomorphism of sections of natural vector bundles are computed in terms of
Lie derivatives along adapted non-autonomous vector fields by extending a key
lemma in [Markus Mauhart, Peter W. Michor: Commutators of flows and fields.
Arch. Math. (Brno) 28 (1992), 228-236. arXiv:math/9204221]. There is also the
analogous result about the first non-vanishing derivative of higher order.

Cet article explore les excursions dans le temps et leurs implications.

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