2014/03/26 by A. T. Filippov
Mathematics · Physics and Astronomy · #gr-qc #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1134/s1547477114070176
15 pages. arXiv admin note: substantial text overlap with arXiv:1302.6372
arxiv created 2014/03/26 · arxiv updated 2015/06/19
We consider the dilaton gravity models derived by reductions of generalized theories of gravity and study one-dimensional dynamical systems simultaneously describing cosmological and static states in any gauge. Our approach is fully applicable to studying static and cosmological solutions in multidimensional theories and also in general one-dimensional dilaton - scalaron gravity models. We here focus on general and global properties of the models, on seeking integrals, and on analyzing the structure of the solution space. We propose some new ideas in this direction and derive new classes of integrals and new integrable models.