A note on the proof of Bertrand's theorem

Vladimir Jovanović

In this paper we fill a common gap in the proof of Bertrand' theorem present both the in Bertrand's original paper \emph{Théorème relatif au movement d'un point attiré vers un centre fixe} and in the Arnold's book \emph{Mathematical methods of classical mechanics}, by providing missing details which pertain to the problem of how to single out elastic and gravitational potentials among the power law ones.