Response to: "Limitations of the Method of Lagrangian Descriptors" [arXiv:1510.04838]

TL;DR

This paper refutes claims that the method of Lagrangian Descriptors fails to detect stable and unstable manifolds, demonstrating that correct application of the method effectively reveals these structures in dynamical systems.

Contribution

The authors clarify the proper application of Lagrangian Descriptors and counter recent criticisms by showing the method's effectiveness in identifying invariant manifolds.

Findings

Lagrangian Descriptors accurately detect stable and unstable manifolds when correctly applied.

Criticism based on misinterpretation of the method is addressed and corrected.

The method remains valid for analyzing hyperbolic trajectories in various systems.

Abstract

This Response is concerned with the recent Comment of Ruiz-Herrera, "Limitations of the Method of Lagrangian Descriptors" [arXiv:1510.04838], criticising the method of Lagrangian Descriptors. In spite of the significant body of literature asserting the contrary, Ruiz-Herrera claims that the method fails to reveal the presence of stable and unstable manifolds of hyperbolic trajectories in incompressible systems and in almost all linear systems. He supports this claim by considering the method of Lagrangian descriptors applied to three specific examples. However in this response we show that Ruiz-Herrera does not understand the proper application and interpretation of the method and, when correctly applied, the method beautifully and unambiguously detects the stable and unstable manifolds of the hyperbolic trajectories in his examples.