Summer School and Conference on Modern Mathematical Physics

## Abstracts
We study dynamical complexity of the Lemaitre-Friedmann-Robertson-Walker cosmological models. As a source of gravity we consider both the minimally and non-minimally coupled to gravity scalar field as well as the barotropic matter. In study of evolutional paths of cosmological models the methods of dynamical systems is used. We investigate also methods of symmetry of Lie groups to study symmetry of dynamical equations. The role of scaling symmetry is investigated in detail in the context of the scalar field cosmology. It will be demonstrated that including of the baraotropic matter and a scalar field gives rise to new evolutional scenarios not expected before. We show the existence in the phase space so called twister type of evolution driven by a non-minimal coupling for which the accelerating universe is a global attractor. The issues of structural stability of the systems are investigated in the context of study of generic and non-generic models in the Ensemble of Dark energy FRW models. We distinguish typical and non-typical evolutional scenarios and argue that a good model of the Universe cannot be necessary generic, i.e. the universe model can be fine-tuned like on the knife edge. |