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Gravitation and Cosmology

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

Asymptotic Poincaré compactification and finite-time singularities

  • Spiros CotsakisEmail author
Article

Abstract

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.

Keywords

Weight Vector Central Projection Dominant Part Maximum Expansion Weighted Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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