text: As noted above under hyperbolic LCSs, a global variational approach has been developed in two dimensions to capture elliptic LCSs as closed stationary curves of the material-line-averaged Lagrangian strain functional. Such curves turn out to be closed null-geodesics of the generalized Green–Lagrange strain tensor family , where  is a positive parameter (Lagrange multiplier). The closed null-geodesics can be shown to coincide with limit cycles of the family of direction fields
  Note that for , the direction field  coincides with the direction field  for shearlines obtained above from the local variational theory of LCSs.
  Trajectories of  are referred to as -lines. Remarkably, they are initial positions of material lines that are infinitesimally uniformly stretching under the flow map . Specifically, any subset of a -line is stretched by a factor of  between the times  and . As an example, Fig. 13 shows elliptic LCSs identified as closed -lines within the Great Red Spot of Jupiter.