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M\"obius transformations and the configuration space of a Hilbert snake
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The purpose of this paper is to give a simpler proof to the problem of controllability of a Hilbert snake \cite{PeSa}. Using the action of the M\"obius group of the unit sphere on the configuration space, in the context of a separable Hilbert space. We give a generalization of the Theorem of accessibility contained in \cite{Ha} and \cite{Ro} for articulated arms and snakes in a finite dimensional Hilbert space
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