Non-integrability of a system with the Dyson Potential

2017/12/01 by Georgiev, Georgi
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.00189

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.

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