Asymptotic Poincar\'e compactification and finite-time singularities
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 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.
Keywords
Cite
@article{arxiv.1301.4778,
title = {Asymptotic Poincar\'e compactification and finite-time singularities},
author = {Spiros Cotsakis},
journal= {arXiv preprint arXiv:1301.4778},
year = {2015}
}
Comments
v2: 14 pages, more references and more discussion, matches version to appear in Grav. Cosm. arXiv admin note: text overlap with arXiv:1212.6737