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

K. Vesely·J. Podolsky
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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.

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K. Vesely, J. Podolsky. 2000-06-19. Chaos in a modified Henon-Heiles system describing geodesics in gravitational waves. https://doi.org/10.1016/s0375-9601(00)00391-1

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