Inverse problem and Bertrand's theorem

Yves Grandati (1) , Alain Bérard (1) , Ferhat Menas (2)

1 LPMC - Laboratoire de physique moléculaire et des collisions
2 LPCQ - Laboratoire de Physique et Chimie Quantique [Tizi-Ouzou]

The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical equation. This permit a particulary compact and elegant proof of Bertrand's theorem.

Mots clés: inverse problem; fractional derivative; Bertrand's theorem

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Mathématiques générales [math.GM]

Yves Grandati, Alain Bérard, Ferhat Menas. Inverse problem and Bertrand's theorem. 2006. ⟨hal-00117494⟩