Note on integrability of certain homogeneous Hamiltonian systems in 2D constant curvature spaces
Exactly Solvable and Integrable Systems
2016-12-23 v2 Mathematical Physics
math.MP
Chaotic Dynamics
Abstract
We formulate the necessary conditions for the integrability of a certain family of Hamiltonian systems defined in the constant curvature two-dimensional spaces. Proposed form of potential can be considered as a counterpart of a homogeneous potential in flat spaces. Thanks to this property Hamilton equations admit, in a general case, a particular solution. Using this solution we derive necessary integrability conditions investigating differential Galois group of variational equations.
Keywords
Cite
@article{arxiv.1606.01084,
title = {Note on integrability of certain homogeneous Hamiltonian systems in 2D constant curvature spaces},
author = {Andrzej J. Maciejewski and Wojciech Szumiński and Maria Przybylska},
journal= {arXiv preprint arXiv:1606.01084},
year = {2016}
}