  We investigate a class of Cardassian scenarios of the universe evolution in
notions of the qualitative theory of dynamical systems. This theory allows 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 $n<0$. Some exact solutions for the flat
Cardassian models as well as a duality relation were found. In turn from the
statistical analysis of Knop's SNIa data, without any priors on matter content
in the model, we obtain that at the 99% confidence level this big-rip scenario
will reach. The potential function for the Hamiltonian description of dynamics
is reconstructed from the SNIa data (inverse dynamical problem). We also
pointed out the statistical analysis results depend oversensitively on the
choice of the model parameter $\mathcal{M}$.
