  We study the quasi-periodic oscillations from the accretion disk around the
distorted Schwarzschild black hole in the framework of the resonant models. We
confine ourselves to the case of a quadrupole distortion which can be caused
for example by the accreting matter flow in the vicinity of the compact object.
For the purpose we examine the linear stability of the circular geodesic orbits
in the equatorial plane and derive analytical expressions for the radial and
vertical epicyclic frequencies. We investigate their properties in comparison
with the isolated Schwarzschild black hole. Due to the influence of the
external matter the vertical epicyclic frequency is not always positive
anymore, and the stability of the circular orbits is determined by the
interplay between both of the frequencies. As a result, the stable circular
orbits do not extend to infinity, but are confined to a finite annular region
between an inner and an outer marginally stable orbit. In addition, the
degeneracy between the vertical epicyclic and the orbital frequency, which is
characteristic for the Schwarzschild solution, is broken, and there are regions
in the parametric space where the radial epicyclic frequency is larger than the
vertical one. All these properties allow for much more diverse types of
non-linear resonances to be excited than for the isolated Schwarzschild black
hole, which can provide an explanation for the observed 3:2 ratio between the
twin-peak frequencies of the quasi-periodic oscillations from the accretion
disk.
