Near Integrability in Low Dimensional Gross--Neveu Models
نویسنده
چکیده
The low-dimensional Gross–Neveu models are studied. For the systems, related to the Lie algebras so(4), so(5), sp(4), sl(3), we prove that they have Birkhoff-Gustavson normal forms which are integrable and non-degenerate in Kolmogorov–Arnold–Moser (KAM) theory sense. Unfortunately, this is not the case for systems with three degrees of freedom, related to the Lie algebras so(6) ∼ sl(4), so(7), sp(6); their Birkhoff–Gustavson normal forms are proven to be non-integrable in the Liouville sense. The last result can easily be extended to higher dimensions.
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تاریخ انتشار 2011