Asymptotic Poincar\'e compactification and finite-time singularities
  We provide an extension of the method of asymptotic decompositions of vector
fields with finite-time singularities by applying the central extension
technique of Poincar\'e to the dominant part of the vector field on approach to
the singularity. This leads to a bundle of fan-out asymptotic systems whose
equilibria at infinity govern the dynamics of the asymptotic solutions of the
original system. We show how this method can be useful to describe a
single-fluid isotropic universe at the time of maximum expansion, and discuss
possible relations of our results to structural stability and non-compact phase
spaces.
