Celestial Mechanics and Dynamical Astronomy

, Volume 112, Issue 2, pp 149–167 | Cite as

Non-integrability of first order resonances in Hamiltonian systems in three degrees of freedom

  • Ognyan Christov
Original Article


The normal forms of the Hamiltonian 1:2:ω resonances to degree three for ω = 1, 3, 4 are studied for integrability. We prove that these systems are non-integrable except for the discrete values of the parameters which are well known. We use the Ziglin–Morales–Ramis method based on the differential Galois theory.


Resonance Non-integrability Morales–Ramis theory 


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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsSofia UniversitySofiaBulgaria

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