Non-integrability of a system with the Dyson Potential

zbMATH Open1424.70012arXiv1712.00189MaRDI QIDQ4627223

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Publication date: 7 March 2019

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.

Full work available at URL: https://arxiv.org/abs/1712.00189

zbMATH Keywords

Hamiltonian systemsDyson potential

Mathematics Subject Classification ID

Hamilton's equations (70H05) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

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