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.