Abstract
This paper shows the results of the investigation of a class of Cardassian scenarios of the evolution of the universe in the formulation of the qualitative theory of dynamical systems. That theory allowed us to analyze all solutions for all possible initial conditions on the phase plane. In the Cardassian models we find that big-rip singularities are present as a typical behavior in the future if n < 0. We were also able to find some exact solution for the flat Cardassian models as well as a duality relation. In turn for the statistical analysis of SNIa data, without any priors on the matter content in the model, we obtain that the big-rip scenario is favored. The potential function for the Hamiltonian description of dynamics was reconstructed from the SNIa data (inverse dynamical problem).
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