The mixmaster universe model, revisited
- 7 August 1994
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 27 (15) , 5357-5361
- https://doi.org/10.1088/0305-4470/27/15/031
Abstract
We re-examine the singularity structure of the mixmaster universe model based on recent developments concerning the treatment of negative resonances. In a previous publication we have shown that this model satisfied the Ablowitz-Ramani-Segur test for the Painleve property. Now using a different method, called the 'perturbative Painleve approach' which involves series in both positive and negative powers of the independent variable, we find that some compatibilities related to negative resonances are not satisfied. This leaves the possibility open that the mixmaster model may be non-integrable.Keywords
This publication has 12 references indexed in Scilit:
- Painleve analysis for the mixmaster universe modelJournal of Physics A: General Physics, 1993
- Analysing negative resonances in the Painlevé testPhysics Letters A, 1991
- The Mixmaster cosmology as a dynamical systemClassical and Quantum Gravity, 1991
- A numerical analysis of chaotic behaviour in Bianchi IX modelsGeneral Relativity and Gravitation, 1990
- Numerical study of initially expanding mixmaster universesClassical and Quantum Gravity, 1990
- Branching of solutions and nonexistence of first integrals in Hamiltonian mechanics. IFunctional Analysis and Its Applications, 1983
- Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. IIFunctional Analysis and Its Applications, 1983
- A connection between nonlinear evolution equations and ordinary differential equations of P-type. IJournal of Mathematical Physics, 1980
- Oscillatory approach to a singular point in the relativistic cosmologyAdvances in Physics, 1970
- Mixmaster UniversePhysical Review Letters, 1969