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. © 2013 Pleiades Publishing, Ltd.
CITATION STYLE
Cotsakis, S. (2013). Asymptotic Poincaré compactification and finite-time singularities. Gravitation and Cosmology, 19(4), 240–245. https://doi.org/10.1134/S0202289313040099
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