Dynamical System Analysis of Cosmologies with Running Cosmological
  Constant from Quantum Einstein Gravity
  We discuss a mechanism that induces a time-dependent vacuum energy on
cosmological scales. It is based on the instability induced renormalization
triggered by the low energy quantum fluctuations in a Universe with a positive
cosmological constant. We employ the dynamical systems approach to study the
qualitative behavior of Friedmann-Robertson-Walker cosmologies where the
cosmological constant is dynamically evolving according with this
nonperturbative scaling at low energies. It will be shown that it is possible
to realize a "two regimes" dark energy phases, where an unstable early phase of
power-law evolution of the scale factor is followed by an accelerated expansion
era at late times.
