This paper presents an (infinite dimensional) geometric framework for control system, based on infinite jet bundles, where a system is represented by a single vector field and dynamic equivalence (to be precise : equivalence by endogenous dynamic feedback) is conjugation by diffeomorphisms. These diffeomorphisms are very much related to Lie-Bäcklund transformations. It is proved in this framework that dynamic equivalence of single-input systems is the same as static equivalence. NB: this paper is followed by "Infinitesimal Brunovsky form for nonlinear systems with applications to dynamic linearization", by E. Aranda-Bricaire, C. H. Moog and J.-B. Pomet, published in the same 1995 volume, which is its natural follow-up. This is a corrected version of the reports http://hal.inria.fr/inria-00074360 and http://hal.inria.fr/inria-00074361.