Secular theory of the orbital evolution of the young stellar disc in the
  Galactic Centre
  We investigate the orbital evolution of a system of N mutually interacting
stars on initially circular orbits around the dominating central mass. We
include perturbative influence of a distant axisymmetric source and an extended
spherical potential. In particular, we focus on the case when the secular
evolution of orbital eccentricities is suppressed by the spherical
perturbation. By means of standard perturbation methods, we derive
semi-analytic formulae for the evolution of normal vectors of the individual
orbits. We find its two qualitatively different modes. Either the orbits
interact strongly and, under such circumstances, they become dynamically
coupled, precessing synchronously in the potential of the axisymmetric
perturbation. Or, if their mutual interaction is weaker, the orbits precess
independently, interchanging periodically their angular momentum, which leads
to oscillations of inclinations. We argue that these processes may have been
fundamental for the evolution of the disc of young stars orbiting the
supermassive black hole in the centre of the Milky Way.
