Analysis reveals variations in escape basin geometry with energy in Hamiltonian systems, suggesting new insights into system behavior.
In this article, we show how the curves that limit the basins of escape in a version of a Hénon–Heiles potential with a singularity at the origin evolve with the energy. The accurate calculation of the sets of asymptotic trajectories to the Lyapunov orbits unveils how the variations in the geometry of the escape regions arise, pointing to a new universal characteristic of open Hamiltonian systems.
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Juan F. Navarro (2025) studied this question.
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