In this paper it is shown that the Hamiltonian system with Dyson potential is analytically non-integrable and formally non-integrable. The approach is based on the following: if the system has a family of periodic solutions around an equilibrium and if the period function is infinitely branched, then the system has no additional analytic first integral. We prove formal non-integrability using Ziglin–Moralez-Ruiz–Ramis theory.
Key words: Dyson potential, Hamiltonian systems
Topic: MATHEMATICS