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Comment on "Nonexistence of the final first integral in the Zipoy-Voorhees space-time"
Georgios Lukes-Gerakopoulos, Andrzej J. Maciejewski, Maria Przybylska +1
The accuracy of the numerical findings of Lukes-Gerakopoulos PRD 86, 044013 (2012), regarding the existence of additional first integrals in the Zipoy-Voorhees space-time, was rece…
Nonexistence of the final first integral in the Zipoy-Voorhees space-time
Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak
We show that the geodesic motion in the Zipoy-Voorhees space-time is not Liouville integrable, in that there does not exist an additional first integral meromorphic in the phase sp…
Global dynamics of cosmological scalar fields -- Part II
Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak +1
This is the second part of integrability analysis of cosmological models with scalar fields. Here, we study systems with conformal coupling, and show that apart from four cases, wh…
Global dynamics of cosmological scalar fields -- Part I
Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak +1
We investigate the Liouvillian integrability of Hamiltonian systems describing a universe filled with a scalar field (possibly complex). The tool used is the differential Galois gr…
Non-integrability of density perturbations in the FRW universe
Tomasz Stachowiak, Marek Szydlowski, Andrzej J. Maciejewski
We investigate the evolution equation of linear density perturbations in the Friedmann-Robertson-Walker universe with matter, radiation and the cosmological constant. The concept o…
On the Integrability of Bianchi Cosmological Models
Andrzej J. Maciejewski, Marek Szydlowski
In this work, we are investigating the problem of integrability of Bianchi class A cosmological models. This class of systems is reduced to the form of Hamiltonian systems with exp…