  The special nonlinear dynamical regimes, "bushes of normal modes", can exist
in the N-particle Hamiltonian systems with discrete symmetry. The dimension of
the bush can be essentially less than that of the whole mechanical system.
One-dimensional bushes represent the similar nonlinear normal modes introduced
by Rosenberg. A given bush can be excited by imposing the appropriate initial
conditions, and the energy of the initial excitation turns out to be trapped in
this bush.
  In the present paper, we consider all possible vibrational bushes in the
simple octahedral mechanical system and discuss their stability under
assumption that the interactions between particles are described by the
Lennard-Jones potential.
