We report our recent results concerning integrability of Hamiltonian systems governed by Hamilton’s function of the form , where the potential V is a finite sum of homogeneous components. In this paper we show how to find, in the differential Galois framework, computable necessary conditions for the integrability of such systems. Our main result concerns potentials of the form , where and are homogeneous functions of integer degrees k and K > k, respectively. We present examples of integrable systems which were obtained by applying our main theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-15,
author = {Andrzej J. Maciejewski and Maria Przybylska},
title = {Overview of the differential Galois integrability conditions for non-homogeneous potentials},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {221-232},
zbl = {1251.37056},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-15}
}
Andrzej J. Maciejewski; Maria Przybylska. Overview of the differential Galois integrability conditions for non-homogeneous potentials. Banach Center Publications, Tome 95 (2011) pp. 221-232. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-15/