Rich Kozai-Lidov Dynamics in an Initially Thin and Eccentric Stellar
  Disc Around a Supermassive Black Hole
  There is growing evidence of star formation in the vicinity of supermassive
black holes (SMBH) in galactic nuclei. A viable scenario for this process
assumes infall of a massive gas cloud towards the SMBH and subsequent formation
of a dense accretion disc which gives birth to the young stars. Numerical
hydrodynamical models indicate that this star formation process is rather fast
and it precedes full circularization of the accretion flow, i.e. the new stars
are born on elliptic orbits. By means of direct numerical N-body modeling, we
show in this paper that the non-zero eccentricity of the stellar discs around
the SMBH leads to an onset of various types of the Kozai-Lidov oscillations of
a non-negligible subset of individual orbits in the disc, showing a remarkable
robustness of this classical mechanism. Among others, we demonstrate that under
certain circumstances, presence of an additional spherical cluster (which is
generally known to damp Kozai-Lidov oscillations) may trigger such oscillations
due to affecting the internal flow of the angular momentum through the disc. We
conclude that the Kozai-Lidov oscillations are capable to substantially modify
the initial structure of the disc (its thickness and distribution of
eccentricities, in particular).
