On the other hand, dynamical systems are often modelled as maps, e.g., [2,3]
where we define the column vectors
The symbol N labels the 
iteration of the map.
Comparing Eqs. (3), (4), (6),
and (7), we see that the
iteration index N can, in some cases, be considered a label for the time
(taken in discrete ``jumps'').
Indeed, a map can be generated from a flow by taking:
where 
is the ``time delay'' [2].
In the right hand part of Eq. (8) we indicate the iterations
corresponding
to the discrete flow times in the left hand side.
In other examples, maps can
arise from flows by taking various types of Poincaré sections, in which
one or more variables are fixed [2].
However, in many cases maps have been constructed as pure dynamical
systems, without recourse to an underlying system of flows. Also, just as
with flows, one can determine whether the map is conservative or
dissipative [2,3].
