Gravitation and Cosmology

, Volume 19, Issue 4, pp 240–245 | Cite as

Asymptotic Poincaré compactification and finite-time singularities

  • Spiros CotsakisEmail author


We provide an extension of the method of asymptotic decompositions of vector fields with finite-time singularities by applying the central extension technique of Poincaré to the dominant part of the vector field at 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.


Weight Vector Central Projection Dominant Part Maximum Expansion Weighted Degree 
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© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Research Group of GeometryDynamical Systems and Cosmology University of the AegeanKarlovassiSamos, Greece

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