Dynamical system analysis at background and perturbation levels:
  Quintessence in severe disadvantage comparing to $\Lambda$CDM
  We perform for the first time a dynamical system analysis of both the
background and perturbation equations, of $\Lambda$CDM cosmology and
quintessence scenario with an exponential potential. In the former case the
perturbations do not change the stability of the late-time attractor of the
background equations, and the system still results in the dark-energy
dominated, de Sitter solution, having passed from the correct dark-matter era
with $\gamma\approx6/11$. However, in the case of quintessence the
incorporation of perturbations changes the stability and properties of the
background evolution, and the only conditionally stable points present either
an exponentially increasing matter clustering not favored by observations, or
Laplacian instabilities, and thus not physically interesting. This result is a
severe disadvantage of quintessence cosmology comparing to $\Lambda$CDM
paradigm.
