Non-integrability of a system with the Dyson Potential

Abstract

In this paper it is shown that the Hamiltonian system with Dyson potential is analytical non-integrable and formal non-integrable. The approach is based on the following: when a system has a family of periodic solutions around an equilibrium and if the period function is infinitely branched then the system has non additional analytic first integral. We prove formal non-integrability using Ziglin-Moralez-Ruiz-Ramis theory.