We define, in an infinite-dimensional differential geometric framework, the "infinitesimal Brunovsky form" which we previously introduced in another framework and link it with equivalence via diffeomorphism to a linear system, which is the same as linearizability by "endogenous dynamic feedback". NB: this paper follows "A differential geometric setting for dynamic equivalence and dynamic linearization", by J.-B. Pomet, published in the same 1995 volume, which is its natural intrduction. This is a corrected version of the reports http://hal.inria.fr/inria-00074360 and http://hal.inria.fr/inria-00074361