Is a pole type singularity an alternative to inflation?
  In this paper, we apply a method of reducing the dynamics of FRW cosmological
models with the barotropic form of the equation of state to the dynamical
system of the Newtonian type to detect the finite scale factor singularities
and the finite-time singularities. In this approach all information concerning
the dynamics of the system is contained in a diagram of the potential function
$V(a)$ of the scale factor. Singularities of the finite scale factor manifest
by poles of the potential function. In our approach the different types of
singularities are represented by critical exponents in the power-law
approximation of the potential. The classification can be given in terms of
these exponents. We have found that the pole singularity can mimick an
inflation epoch. We demonstrate that the cosmological singularities can be
investigated in terms of the critical exponents of the potential function of
the cosmological dynamical systems. We assume the general form of the model
contains matter and some kind of dark energy which is parameterized by the
potential. We distinguish singularities (by ansatz about the Lagrangian) of the
pole type with the inflation and demonstrate that such a singularity can appear
in the past.
