Dynamics in the Kepler problem on the Heisenberg group
Dynamical Systems
2024-06-11 v2 Mathematical Physics
math.MP
Abstract
We study the nonholonomic motion of a point particle on the Heisenberg group around the fixed "sun" whose potential is given by the fundamental solution of the sub-Laplacian. Unlike arXiv:1212.2713 where the variational problem is studied we consider the equations of nonholonomic dynamics which are not Hamiltonian. We find three independent first integrals of the system and show that its bounded trajectories of the system are wound up around certain surfaces of the fourth order.
Cite
@article{arxiv.2311.15746,
title = {Dynamics in the Kepler problem on the Heisenberg group},
author = {Sergey Basalaev and Sergei Agapov},
journal= {arXiv preprint arXiv:2311.15746},
year = {2024}
}
Comments
Some incorrect formulas are fixed in the second version of the preprint