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

A Hamiltonian system with a modified Hénon-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 Hénon-Heiles and the monkey saddle systems are discussed. The box-counting dimension of the basin boundaries is also calculated.