  Study of continuous dynamical system through Poincare map is one of the most
popular topics in nonlinear analysis. This is done by taking intersections of
the orbit of flow by a hyper-plane parallel to one of the coordinate
hyper-planes of co-dimension one. Naturally for a 3D-attractor, the Poincare
map gives rise to 2D points, which can describe the dynamics of the attractor
properly. In a very special case, sometimes these 2D points are considered as
their 1D-projections to obtain a 1D map. However, this is an artificial way of
reducing the 2D map by dropping one of the variables. Sometimes it is found
that the two coordinates of the points on the Poincare section are functionally
related. This also reduces the 2D Poincare map to a 1D map. This reduction is
natural, and not artificial as mentioned above. In the present study, this
issue is being highlighted. In fact, we find out some examples, which show that
even this natural reduction of the 2D Poincare map is not always justified,
because the resultant 1D map may fail to generate the original dynamics. This
proves that to describe the dynamics of the 3D chaotic attractor, the minimum
dimension of the Poincare map must be two, in general.
