Möbius transformations and the configuration space of a Hilbert snake

The purpose of this paper is to give a simpler proof to the problem of controllability of a Hilbert snake [13]. Using the action of the Möbius group of the unite sphere on the configuration space, in the context of a separable Hilbert space, we give a generalization of the theorem of accessibility contained in [9] and [14] for articulated arms and snakes in a finite dimensional Hilbert space.