Dynamical complexity of the Brans-Dicke cosmology
  The dynamics of the Brans-Dicke theory with a quadratic scalar field
potential function and barotropic matter is investigated. The dynamical system
methods are used to reveal complexity of dynamical evolution in homogeneous and
isotropic cosmological models. The structure of phase space crucially depends
on the parameter of the theory $\omega_{\textrm{BD}}$ as well as barotropic
matter index $w_{m}$. In our analysis these parameters are treated as
bifurcation parameters. We found sets of values of these parameters which lead
to generic evolutional scenarios. We show that in isotropic and homogeneous
models in the Brans-Dicke theory with a quadratic potential function the de
Sitter state appears naturally. Stability conditions of this state are fully
investigated. It is shown that these models can explain accelerated expansion
of the Universe without the assumption of the substantial form of dark matter
and dark energy. The Poincare construction of compactified phase space with a
circle at infinity is used to show that phase space trajectories in a physical
region can be equipped with a structure of a vector field on nontrivial
topological closed space. For $\omega_{\textrm{BD}}<-3/2$ we show new types of
early and late time evolution leading from the anti-de Sitter to the de Sitter
state through an asymmetric bounce. In the theory without a ghost we find
bouncing solutions and the coexistence of the bounces and the singularity.
Following the Peixoto theorem some conclusions about structural stability are
drawn.
