  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.
