On the Kepler problem on the Heisenberg group

Sergey Basalaev, Sergei Agapov

Published 2023-11-27Version 1

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.