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

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.

11 pages, 7 figures, LaTeX. To appear in Phys. Lett. A

References in corpus (1)

• Expanding impulsive gravitational waves

Cited by in corpus (9)

• Gyratonic pp-waves and their impulsive limit
• Geodesic motion around a distorted static black hole
• Exact Parallel Waves in General Relativity
• Integrable Henon-Heiles Hamiltonians: a Poisson algebra approach
• Hidden symmetries from distortions of the conformal structure
• Chaotic motion in Kundt spacetimes
• On the dynamics of a seventh-order generalized Hénon-Heiles potential
• Fractal basins of convergence of a seventh-order generalized Hénon-Heiles potential
• Chaotic resetting: A resetting strategy for deterministic chaotic systems