Note on integrability of certain homogeneous Hamiltonian systems in 2D constant curvature spaces

Andrzej J. Maciejewski; Wojciech Szumiński; Maria Przybylska

doi:10.1016/j.physleta.2016.12.030

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arXiv · 1606.01084

Note on integrability of certain homogeneous Hamiltonian systems in 2D constant curvature spaces

Andrzej J. Maciejewski·Wojciech Szumiński·Maria Przybylska

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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.

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Andrzej J. Maciejewski, Wojciech Szumiński, Maria Przybylska. 2016-12-22. Note on integrability of certain homogeneous Hamiltonian systems in 2D constant curvature spaces. https://doi.org/10.1016/j.physleta.2016.12.030

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