Shape Coherence and Finite-Time Curvature Evolution

We introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal the dramatic change on shape such as the folding behaviors in a system. The level curves of the finite-time curvature evolution field indicate the existence of shape coherent sets.