Lagrangian descriptors and their applications to deterministic chaos

TL;DR

This paper reviews recent advances in Lagrangian descriptors, a method based on orbit length over finite times, for distinguishing ordered from chaotic trajectories in dynamical systems, applicable to both discrete and continuous cases.

Contribution

It introduces recent theoretical developments in Lagrangian descriptors and explores their application to planetary dynamics, enhancing chaos detection methods.

Findings

Effective discrimination between ordered and chaotic trajectories

Applicability to both discrete and continuous systems

Insight into planetary dynamics through trajectory analysis

Abstract

We present our recent contributions to the theory of Lagrangian descriptors for discriminating ordered and deterministic chaotic trajectories. The class of Lagrangian Descriptors we are dealing with is based on the Euclidean length of the orbit over a finite time window. The framework is free of tangent vector dynamics and is valid for both discrete and continuous dynamical systems. We review its last advancements and touch on how it illuminated recently Dvorak's quantities based on maximal extent of trajectories' observables, as traditionally computed in planetary dynamics.