Asymptotic Poincaré 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 Poincaré 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.

v2: 14 pages, more references and more discussion, matches version to appear in Grav. Cosm. arXiv admin note: text overlap with arXiv:1212.6737

References in corpus (6)

• The Dominant Balance at Cosmological Singularities
• Cosmological Singularities and Bel-Robinson Energy
• Brane singularities and their avoidance
• Asymptotics of flat, radiation universes in quadratic gravity
• Singularities in cosmologies with interacting fluids
• Brane singularities with mixtures in the bulk

Cited by in corpus (3)

• Cosmic dynamics and qualitative study of Rastall model with spatial curvature
• $\mathcal{N}$-field cosmology in hyperbolic field space: stability and general solutions
• Interacting vacuum at infinity