  A characterization of the two-terminal open-ring Aharonov-Bohm interferometer
is made by analyzing the phase space plots in the complex transmission
amplitude plane. Two types of plots are considered: type I plot which uses the
magnetic flux as the variable parameter and type II plot which uses the
electron momentum as the variable parameter. In type I plot, the trajectory
closes upon itself only when the ratio $R$ of the arm lengths (of the
interferometer) is a rational fraction, the shape and the type of the generated
flower-like pattern is sensitive to the electron momentum. For momenta
corresponding to discrete eigenstates of the perfect ring (i.e. the ring
without the leads), the trajectory passes through the origin a certain fixed
number of times before closing upon itself, whereas for arbitrary momenta it
never passes through the origin. Although the transmission coefficient is
periodic in the flux with the elementary flux quantum as the basic period, the
phenomenon of electron transmission is shown not to be so when analyzed via the
present technique. The periodicity is seen to spread over several flux units
whenever $R$ is a rational fraction whereas there is absolutely no periodicity
present when $R$ is an irrational number. In type II plot, closed trajectories
passing through the origin a number of times are seen for $R$ being a rational
fraction. The case R=1 (i.e. a symmetric ring) with zero flux is rather
pathological--it presents a closed loop surrounding the origin. For irrational
$R$ values, the trajectories never close.
