Poincaré Map
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.
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dynamical systems
