  ecent observations of type Ia supernovae indicate that the Universe is in an
accelerating phase of expansion. The fundamental quest in theoretical cosmology
is to identify the origin of this phenomenon. In principle there are two
possibilities: 1) the presence of matter which violates the strong energy
condition (a substantial form of dark energy), 2) modified Friedmann equations
(Cardassian models -- a non-substantial form of dark matter). We classify all
these models in terms of 2-dimensional dynamical systems of the Newtonian type.
We search for generic properties of the models. It is achieved with the help of
Peixoto's theorem for dynamical system on the Poincar{\'e} sphere. We find that
the notion of structural stability can be useful to distinguish the generic
cases of evolutional paths with acceleration. We find that, while the
$\Lambda$CDM models and phantom models are typical accelerating models, the
cosmological models with bouncing phase are non-generic in the space of all
planar dynamical systems. We derive the universal shape of potential function
which gives rise to presently accelerating models. Our results show explicitly
the advantages of using a potential function (instead of the equation of state)
to probe the origin of the present acceleration. We argue that simplicity and
genericity are the best guide in understanding our Universe and its
acceleration.
