Consider an 
-dimensional
deterministic dynamical system
 |
and let 
be an 
-dimensional
surface of section that is traverse to the flow,
i.e., all trajectories starting from 
flow through it and are not parallel to it. Then a Poincaré
map 
is a mapping from 
to itself obtained by following trajectories from one intersection
of the surface 
to the next. Poincaré maps are useful when studying swirling flows near periodic
solutions in dynamical systems.
