A proof of Bertrand's theorem using the theory of isochronous potentials

TL;DR

This paper provides an alternative proof of Bertrand's theorem by leveraging the concept of isochronicity in a specific family of centers, offering a new perspective on classical mechanics.

Contribution

It introduces a novel proof of Bertrand's theorem based on the theory of isochronous potentials, connecting classical results with modern dynamical systems theory.

Findings

Proof of Bertrand's theorem via isochronicity

Identification of a family of centers with isochronous properties

New insights into classical potential problems

Abstract

We give an alternative proof for the celebrated Bertrand's theorem as a corollary of the isochronicity of a certain family of centers.