2008/03/31 by Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak +1
Physics and Astronomy · Mathematics · #math-ph #gr-qc #math.MP #nlin.SI #msc:37J30 #msc:70H06 #msc:70H07
paper · pdf · doi:10.1088/1751-8113/41/46/465101
published as J.Phys.A41:465101,2008 · This is a conflated version of arXiv:gr-qc/0612087 and arXiv:gr-qc/0703031 with a new theory section
arxiv created 2008/08/19 · arxiv updated 2009/12/01
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 group approach, as introduced by Morales-Ruiz and Ramis. The main result is that the generic systems with minimal coupling are non-integrable, although there still exist some values of parameters for which integrability remains undecided; the conformally coupled systems are only integrable in four known cases. We also draw a connection with chaos present in such cosmological models, and the issues of integrability restricted to the real domain.