  We perform a phase-space analysis of the cosmological 3-fluid problem
consisting of a barotropic fluid with an equation-of-state parameter
$\gamma-1$, a pressureless dark matter fluid, plus a scalar field $\phi$
(representing dark energy) coupled to exponential potential
$V=V_0\exp{(-\kappa\lambda\phi)}$. Besides the potential-kinetic-scaling
solutions, which are not the unique late-time attractors whenever they exist
for $\lambda^2\geq 3\ga$, we derive new attractors where both dark energy and
dark matter coexist and the final density is shared in a way independent of the
value of $\gamma >1$. The case of a pressureless barotropic fluid ($\gamma =1$)
has a one-parameter family of attractors where all components coexist. New
one-parameter families of matter-dark matter saddle points and kinetic-matter
repellers exist. We investigate the stability of the ten critical points by
linearization and/or Lyapunov's Theorems and a variant of the theorems
formulated in this paper. A solution with two transient periods of acceleration
and two transient periods of deceleration is derived.
