Comment on "finding finite-time invariant manifolds in two-dimensional velocity fields" [chaos 10, 99 (2000)]

This note serves as a commentary of the paper of Haller [Chaos 10, 99 (2000)] on techniques for detecting invariant manifolds. Here we show that the criterion of Haller can be improved in two ways. First, by using the strain basis reference frame, a more efficient version of theorem 1 of Haller (2000) allows to better detect the manifolds. Second, we emphasize the need to nondimensionalize the estimate of hyperbolic persistence. These statements are illustrated by the example of the Kida ellipse.