The applicability of the third integral of motion: Some numerical experiments

@article{Hnon1964TheAO,
title={The applicability of the third integral of motion: Some numerical experiments},
author={Michel H{\'e}non and Carl Heiles},
journal={The Astronomical Journal},
year={1964},
volume={69},
pages={73-79}
}

The problem of the existence of a third isolating integral of motion in an axisymmetric potential is investigated by numerical experiments. It is found that the third integral exists for only a limited rage of initial conditions.

Abstract An analytical expression for a third integral of motion in an rotationally symmetric potential is derived. This expression is constant along trajectories.

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