# Finding NHIM in 2 and 3 degrees-of-freedom with H\'enon-Heiles type potential

## TL;DR

This paper demonstrates how Lagrangian descriptors can effectively identify high-dimensional phase space structures like NHIMs in Hamiltonian systems with 2 and 3 degrees of freedom, aiding understanding of phase space transport.

## Contribution

It introduces a novel application of Lagrangian descriptors to reveal NHIMs and their manifolds in high-dimensional Hamiltonian systems with practical implications.

## Key findings

- Lagrangian descriptors successfully identify NHIMs in 2 and 3 DOF systems.
- The method reveals stable and unstable manifolds acting as phase space barriers.
- Applications extend to physics and chemistry systems.

## Abstract

We present the capability of Lagrangian descriptors for revealing the high dimensional phase space structures that are of interest in nonlinear Hamiltonian systems with index-1 saddle. These phase space structures include normally hyperbolic invariant manifolds and their stable and unstable manifolds, and act as codimenision-1 barriers to phase space transport. The method is applied to classical two and three degrees-of-freedom Hamiltonian systems which have implications for myriad applications in physics and chemistry.