  We propose rotation inferred from the polar decomposition of the flow
gradient as a diagnostic for elliptic (or vortex-type) invariant regions in
non-autonomous dynamical systems. We consider here two- and three-dimensional
systems, in which polar rotation can be characterized by a single angle. For
this polar rotation angle (PRA), we derive explicit formulas using the singular
values and vectors of the flow gradient. We find that closed level sets of the
PRA reveal elliptic islands in great detail, and singular level sets of the PRA
uncover centers of such islands. Both features turn out to be objective
(frame-invariant) for two-dimensional systems. We illustrate the diagnostic
power of PRA for elliptic structures on several examples.
