General dynamical properties of cosmological models with nonminimal
  kinetic coupling
  We consider cosmological dynamics in the theory of gravity with the scalar
field possessing the nonminimal kinetic coupling to curvature given as $\eta
G^{\mu\nu}\phi_{,\mu}\phi_{,\nu}$, where $\eta$ is an arbitrary coupling
parameter, and the scalar potential $V(\phi)$ which assumed to be as general as
possible. With an appropriate dimensionless parametrization we represent the
field equations as an autonomous dynamical system which contains ultimately
only one arbitrary function $\chi (x)= 8 \pi \vert \eta \vert V(x/\sqrt{8
\pi})$ with $x=\sqrt{8 \pi}\phi$. Then, assuming the rather general properties
of $\chi(x)$, we analyze stationary points and their stability, as well as all
possible asymptotical regimes of the dynamical system. It has been shown that
for a broad class of $\chi(x)$ there exist attractors representing three
accelerated regimes of the Universe evolution, including de Sitter expansion
(or late-time inflation), the Little Rip scenario, and the Big Rip scenario. As
the specific examples, we consider a power-law potential
$V(\phi)=M^4(\phi/\phi_0)^\sigma$, Higgs-like potential
$V(\phi)=\frac{\lambda}{4}(\phi^2-\phi_0^2)^2$, and exponential potential
$V(\phi)=M^4 e^{-\phi/\phi_0}$.
