2021/02/19 by Primitivo B. Acosta-Humánez, Acosta-Humánez, Primitivo, Juan J. Morales-Ruiz +3 · 1 citation
Mathematics · Physics and Astronomy · #34M25 #35A22 #35C05 #92D25 #Advanced Differential Equations and Dynamical Systems #Black Holes and Theoretical Physics #Cosmological constant #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Integrable system #Invariant (physics) #Isotropy #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Quantum mechanics #Singularity
paper · pdf · doi:10.48550/arxiv.2102.10108
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2021/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the integrability of an anisotropic universe with matter and cosmological constant formulated as Bianchi IX models. The presence of the cosmological constant causes the existence of a critical point in the finite part of the phase space. The separatrix associated to this Einstein's static universe is entirely contained in an invariant isotropic plane forgetting the singularity at the origin. This invariant plane of isotropy is an integrable sub-space of the Taub type. In this paper we analyse the differential Galois group of the second order variational equations to this plane in order to apply the integrability theorem of the second author with Ramis and Sim' o. The main result is that the model is non-integrable by meromorphic functions.