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

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

Feb 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012cemda.112..149c&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 112, Issue 2, pp.149-167

Astronomy and Astrophysics

Astronomy

Resonance, Non-Integrability, Morales-Ramis Theory

Scientific paper

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.

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