The aim of this paper is to present two examples of non academic Hamiltonian systems for which the Morales-Ramis theory can be applied effectively. First, we investigate the Gross-Neveu system with n degrees of freedom. Till now it has been proved that this system is not integrable for n = 3. We give a simple proof that it is not completely integrable for an arbitrary n ≥ 3. Our second example is a natural generalisation of the Jacobi problem of a material point moving on an ellipsoid. We formulate sufficient conditions for its non-integrability.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc58-0-10,
author = {Andrzej J. Maciejewski},
title = {Non-integrability of certain Hamiltonian systems. Applications of the Morales-Ramis differential Galois extension of Ziglin theory},
journal = {Banach Center Publications},
volume = {58},
year = {2002},
pages = {139-150},
zbl = {1033.37028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc58-0-10}
}
Andrzej J. Maciejewski. Non-integrability of certain Hamiltonian systems. Applications of the Morales-Ramis differential Galois extension of Ziglin theory. Banach Center Publications, Tome 58 (2002) pp. 139-150. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc58-0-10/