Revisiting dynamics of interacting quintessence
  We apply the tools of the dynamical system theory in order to revisit and
uncover the structure of a nongravitational interaction between pressureless
dark matter and dark energy described by a scalar field $\phi$. For a coupling
function $Q = -(\alpha d\rho_m/dt + \beta d\rho_\phi/dt )$, where t is the
cosmic time, we have found that it can be rewritten in the form $Q = 3H (\alpha
\rho_m + \beta (d\phi/dt)^2 )/(1-\alpha +\beta)$, so that its dependence on the
dark matter density and on the kinetic term of the scalar field is linear and
proportional to the Hubble parameter. We analyze the scenarios $\alpha=0$,
$\alpha = \beta$ and $\alpha = -\beta$, separately and in order to describe the
cosmological evolution we have calculated various observables. A notable result
of this work is that, unlike for the noninteracting scalar field with
exponential potential where five critical points appear, in the case studied
here, with the exception of the matter dominated solution, the remaining
singular points are transformed into scaling solutions enriching the phase
space. It is shown that for $\alpha \neq 0$, a separatrix arises modifying
prominently the structure of the phase space. This represents a novel feature
no mentioned before in the literature.
