  The identification and visualization of Lagrangian structures in flows plays
a crucial role in the study of dynamic systems and fluid dynamics. The Finite
Time Lyapunov Exponent (FTLE) has been widely used for this purpose; however,
it only approximates the flow by considering the positions of particles at the
initial and final times, ignoring the actual trajectory of the particle. To
overcome this limitation, we propose a novel quantity that extends and
generalizes the FTLE by incorporating trajectory metrics as a measure of
similarity between trajectories. Our proposed method utilizes trajectory
metrics to quantify the distance between trajectories, providing a more robust
and accurate measure of the LCS. By incorporating trajectory metrics, we can
capture the actual path of the particle and account for its behavior over time,
resulting in a more comprehensive analysis of the flow. Our approach extends
the traditional FTLE approach to include trajectory metrics as a means of
capturing the complexity of the flow.
