  We investigate the classical dynamics of a Rydberg hydrogen atom near the
surface of a planar topological insulator. The system is described by a
Hamiltonian consisting of the free-hydrogen part and the hydrogen-surface
potential. The latter includes the interactions between the electron and both
image electric charges and image magnetic monopoles. Owing to the axial
symmetry, the $z$ component of angular momentum $l_{z}$ is conserved. Here we
consider the $l_{z} = 0$ case. The structure of the phase space is explored
extensively by means of numerical techniques and Poincar\'{e} surfaces of
section for the recently discovered topological insulator TlBiSe$_{2}$. The
phase space of the system is separated into regions of vibrational and
rotational motion. We show that vibrational-rotational-vibrational type
transitions can be tuned with the topological magnetoelectric polarizability.
