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The aim of this work is to revise but also explore even further the escapedynamics in the H\'{e}non-Heiles system. In particular, we conduct a thoroughand systematic numerical investigation distinguishing between trapped (orderedand chaotic) and escaping orbits, considering only unbounded motion for severalenergy levels. It is of particular interest, to locate the basins of escapetowards the different escape channels and relate them with the correspondingescape periods of the orbits. In order to elucidate the escape process weconduct a thorough investigation in several types of two-dimensional planes andalso in a three-dimensional subspace of the entire four-dimensional phasespace. We classify extensive samples of orbits by integrating numerically theequations of motion as well as the variational equations. In an attempt todetermine the regular or chaotic nature of trapped motion, we apply the SALImethod, as an accurate chaos detector. It was found, that in all studied casesregions of non-escaping orbits coexist with several basins of escape. Most ofthe current outcomes have been compared with previous related work.

An overview of the escape dynamics in the Henon-Heiles Hamiltonian system