  A simple geometrical model is presented for the gravity-driven motion of a
single particle on a rough inclined surface. Adopting a simple restitution law
for the collisions between the particle and the surface, we arrive at a model
in which the dynamics is described by a one-dimensional map. This map is
studied in detail and it is shown to exhibit several dynamical regimes (steady
state, chaotic behavior, and accelerated motion) as the model parameters vary.
A phase diagram showing the corresponding domain of existence for these regimes
is presented. The model is also found to be in good qualitative agreement with
recent experiments on a ball moving on a rough inclined line.

Soft Condensed Matter