Astronomy and Astrophysics – Astronomy
Scientific paper
Jul 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994mnras.269..127m&link_type=abstract
Monthly Notices of the Royal Astronomical Society, Vol. 269, NO. 1/JUL1, P. 127, 1994
Astronomy and Astrophysics
Astronomy
5
Scientific paper
The complexity of the study of the three-body problem is reduced by choosing initial values along curves in phase space. This way, the results can be expressed in terms of simple curves demonstrating the behaviour of the final evolution of the trajectories. This method allows a new kind of study of the nature of the behaviour of three-body systems. When a trajectory is characterized by the type of final motion, one sees regular and apparently chaotic regions in phase space. Transition to sensitive dependence on mitial conditions occurs at hypersurfaces of parabolic disruption. (The final state is a binary plus a single particle escaping at an asymptotically parabolic speed.) Regular regions are characterized by short interplay times and continuous variation of the parameters of the final motion, while the chaotic orbits are associated with long interplay times. The distribution of final-state binding energies remains the same if initial values are chosen along a short length of curve in a chaotic region or are scattered randomly in phase space. It is concluded that the phase space is divided into separate zones by hypersurfaces of parabolic disruption. On these hypersurfaces the dependence on initial conditions is discontinuous, while between such surfaces the final motion depends in a continuous manner on initial conditions. The chaotic sections are not really chaotic, but in these regions the disconnecting singular surfaces are very dense, such that practical unpredictability occurs. Key words: chaotic phenomena - methods: numerical - celestial mechanics, stellar dynamics.
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