  We demonstrate a model-independent method of estimating qualitative dynamics
of an accelerating universe from observations of distant type Ia supernovae.
Our method is based on the luminosity-distance function, optimized to fit
observed distances of supernovae, and the Hamiltonian representation of
dynamics for the quintessential universe with a general form of equation of
state $p=w(a(z))\rho$. Because of the Hamiltonian structure of FRW dynamics
with the equation of state $p = w(a(z)) \rho$, the dynamics is uniquelly
determined by the potential function $V(a)$ of the system. The effectiveness of
this method in discrimination of model parameters of Cardassian evolution
scenario is also given. Our main result is the following, restricting to the
flat model with the current value of $\Omega_{m,0}=0.3$, the constraints at
$2\sigma$ confidence level to the presence of $\rho^{n}$ modification of the
FRW models are $-0.50 \lesssim n \lesssim 0.36$.
