Using Lagrangian descriptors to uncover invariant structures in Chesnavich's Isokinetic Model with application to roaming

TL;DR

This paper demonstrates how Lagrangian descriptors can be used to identify invariant manifolds in complex dynamical systems, specifically applied to the Chesnavich CH4+ model to analyze roaming phenomena.

Contribution

The study introduces a novel application of Lagrangian descriptors to locate invariant structures in highly unstable periodic orbits within the Chesnavich model.

Findings

Successfully identified invariant manifolds in the Chesnavich model.

Enabled analysis of roaming dynamics through invariant structures.

Low computational cost of the method facilitates complex system analysis.

Abstract

Complementary to existing applications of Lagrangian descriptors as an exploratory method, we use Lagrangian descriptors to find invariant manifolds in a system where some invariant structures have already been identified. In this case we use the parametrisation of a periodic orbit to construct a Lagrangian descriptor that will be locally minimised on its invariant manifolds. The procedure is applicable (but not limited) to systems with highly unstable periodic orbits, such as the isokinetic Chesnavich CH4+ model subject to a Hamiltonian isokinetic theromostat. Aside from its low computational requirements, the method enables us to study the invariant structures responsible for roaming in the isokinetic Chesnavich CH4+ model.