# The Mixmaster Universe: the final reckoning?

@article{Andriopoulos2008TheMU, title={The Mixmaster Universe: the final reckoning?}, author={Konstantinos Andriopoulos and P. G. L. Leach}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2008}, volume={41}, pages={155201} }

The investigation of the Mixmaster Universe using singularity analysis has attracted much attention in recent years and produced a variety of interpretations, some of which have been supported by numerical experimentation. We present a new singularity analysis and make direct comparisons with systems of known dynamical behaviour to avoid making unwarranted inferences and remove the controversy surrounding the Mixmaster Universe.

## 15 Citations

### The occurrence of a triple -1 resonance in the standard singularity analysis

- Physics
- 2008

Any careful singularity analysis of the Mixmaster Universe uncovers the instance of a triple -1 resonance. The Mixmaster Universe does not exhibit a closed-form solution and so a correct…

### BKL Method in the Bianchi IX Universe Model Revisited

- Physics
- 2013

Given the extreme difficulty in finding analytical solutions to Einstein’s equations for universe models, such as the Bianchi type IX, different physical-mathematical techniques have been designed to…

### Free Motion around Black Holes with Disks or Rings: Between Integrability and Chaos–V

- PhysicsThe Astrophysical Journal
- 2019

The complete integrability of geodesic motion, the well-known feature of fields of isolated stationary black holes, can easily be “spoiled” by the presence of some additional sources (even if highly…

### Cosmological singularities and analytical solutions in varying vacuum cosmologies

- PhysicsThe European Physical Journal C
- 2018

We investigate the dynamical features of a large family of running vacuum cosmologies for which $$\Lambda $$Λ evolves as a polynomial in the Hubble parameter. Specifically, using the critical point…

### Integrability of the mixmaster model

- MathematicsPhysical Review D
- 2019

We make use of a generalized definition of a class of nonlocal conserved charges in phase space to demonstrate that the anisotropic Bianchi type IX model in vacuum is (at least locally) Liouville…

### New insights into singularity analysis

- MathematicsInternational Journal of Nonlinear Sciences and Numerical Simulation
- 2021

Abstract In this work, we emphasize the use of singularity analysis in obtaining analytic solutions for equations for which standard Lie point symmetry analysis fails to make any lucid decision. We…

### Quantum cosmology of Bianchi VIII, IX LRS geometries

- MathematicsJournal of Cosmology and Astroparticle Physics
- 2019

In the present work we revisit the axisymmetric Bianchi VIII and IX models. At the classical level we reproduce the known analytic solution, in a novel way making use of two quadratic integrals of…

### Bianchi IX cosmologies in the Einstein-Skyrme system in a sector with nontrivial topological charge

- PhysicsPhysical Review D
- 2019

The dynamics of the most general Bianchi IX cosmology with three time dependent scale factors for the Einstein-Skyrme system is analyzed. For the Skyrmion, a generalized hedgehog ansatz with unit…

### Free motion around black holes with discs or rings: between integrability and chaos - II: Chaos around black holes with discs or rings

- Physics
- 2010

Geodesic dynamics is regular in the fields of isolated statio n ry black holes. However, due to the presence of unstable periodic orbits, it easily becomes chaotic under various perturbations. Here…

### Singularity and symmetry analyses of mathematical models of epidemics.

- Mathematics
- 2010

We present a summary of the methods of Lie symmetry and Painleve singularity analyses and apply them to a number of wellknown epidemiological models to demonstrate the utility of these analyses in…

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