Shape Coherence and Finite-Time Curvature Evolution

TL;DR

This paper introduces a new concept of finite-time curvature evolution to analyze shape coherence in dynamical systems, revealing shape changes like folding and identifying coherent sets through curvature level curves.

Contribution

It presents a novel definition of finite-time curvature evolution and demonstrates its effectiveness in detecting shape coherence and dramatic shape changes in dynamical systems.

Findings

Finite-time curvature growth points indicate shape changes like folding.

Level curves of curvature evolution reveal shape coherent sets.

The method distinguishes between slow curvature preservation and rapid shape transformations.

Abstract

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.