  One of the problems for the cyclic Universe will be its compatibility with a
vast population of indestructible black holes that accumulate from cycle to
cycle. The article considers a simple iterative model of the evolution of black
holes in a cyclic Universe, independent of specific cosmological theories. The
model has two free parameters that determine the iterative decrease in the
number of black holes and the increase in their individual mass. It is shown
that this model, with wide variations in the parameters, explains the observed
number of supermassive black holes at the centers of galaxies, as well as the
relationships between different classes of black holes. The mechanism of
accumulation of relict black holes during repeated pulsations of the Universe
may be responsible for the black hole population detected by LIGO observations
and probably responsible for the dark matter phenomenon. The number of black
holes of intermediate masses corresponds to the number of globular clusters and
dwarf satellite galaxies. These results argue for models of the oscillating
Universe, and at the same time impose substantial requirements on them. Models
of a pulsating Universe should be characterized by a high level of relict
gravitational radiation generated at the time of maximum compression of the
Universe and mass mergers of black holes, as well as solve the problem of the
existence of the largest black hole that is formed during this merger. It has
been hypothesized that some neutron stars can survive from past cycles of the
Universe and contribute to dark matter. These relict neutron stars will have a
set of features by which they can be distinguished from neutron stars born in
the current cycle of the birth of the Universe. The observational signs of
relict neutron stars and the possibility of their search in different
wavelength ranges are discussed.
