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The paper aims at a demonstration of the principal differences between the oscillation spectra of multi-component systems and a one-component medium. The character of the mutual motions of components appears then to be of importance. Three cases are considered: (1) motionless components in the inertial frame of reference; (2) inertial subsystems moving at constant relative velocities; (3) a rotating n-component system. The oscillation spectra in these three cases have qualitative differences between each other and when compared with those of resting or rotating one-component systems.
An estimate for the slow bar instability boundary for a generalized disk polytropic model is derived. The effects of a spherical halo are studied: it turns out that a halo can be favorable to this instability (at the same time suppressing the bending instability).
Stability of spherical and thin disk stellar clusters surrounding massive black holes are studied. Due to the black hole, stars with sufficiently low angular momenta escape from the system through the loss cone. We show that stability of spherical clusters crucially depend on whether the distribution of stars is monotonic or non-monotonic in angular momentum. It turns out that only non-monotonic distributions can be unstable. At the same time the instability in disk clusters is possible for both types of distributions.
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