| Theory | Measures | Design | Related Keywords |
| Shape coherent sets | Shape coherence factor | Preserving shape. Regularity link between curvature and shape coherence | Finite-time stable/unstable foliation, nonhyperbolic splitting angles, slow evolving curvature, FTC. |
| Geodesic transport barrier | Arc length evolution | Stationary values of the averaged strain and the averaged shear | Hyperbolic, elliptic and parabolic barriers Lagrangian coherent structures. [9] [16] [17] |
| Coherent pairs | Coherent pair number | Minimizing density loss, Frobenius-Perron operator by Ulam-Galerkin’s matrix, SVD | Coherent pairs, hierarchical partitions, Galerkin-Ulam matrices. [2] [12] [21] |