Chaos in a modified Henon-Heiles system describing geodesics in gravitational waves

TL;DR

This paper investigates chaos in a modified Henon-Heiles Hamiltonian system modeling test particle motion in gravitational wave spacetimes, revealing fractal basin boundaries and chaos at high energies.

Contribution

It introduces a modified Henon-Heiles model for geodesics in gravitational waves and analyzes its chaotic behavior and basin boundary fractality.

Findings

Chaos occurs at energies above a threshold.

Basins of escape have fractal boundaries.

Box-counting dimension quantifies boundary complexity.

Abstract

A Hamiltonian system with a modified Henon-Heiles potential is investigated. This describes the motion of free test particles in vacuum gravitational pp-wave spacetimes with both quadratic ("homogeneous") and cubic ("non-homogeneous") terms in the structural function. It is shown that, for energies above a certain value, the motion is chaotic in the sense that the boundaries separating the basins of possible escapes become fractal. Similarities and differences with the standard Henon-Heiles and the monkey saddle systems are discussed. The box-counting dimension of the basin boundaries is also calculated.