Dynamical Systems theory is a valuable tool in the profound study of Cosmology, as qualitative methods allow to characterize cosmological solutions on the basis of their relevant physical features (e.g. stability and asymptotic behaviour). Here we briefly review some well established results for cosmological models in the framework of General Relativity. Then we consider a family of modified cosmological models which are gaining more and more relevance, namely Loop Quantum Cosmologies. In particular we analyze the geometrical structure and dynamical properties of the model presented in earlier.
"Dynamical Systems Techniques in Cosmology. An Example: LQC and the Einstein Static Universe." J. Geom. Symmetry Phys. 14 67 - 83, 2009. https://doi.org/10.7546/jgsp-14-2009-67-83