Can the integrability of Hamiltonian systems be decided by the knowledge of scattering data?

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Abstract
A method is proposed to show how scattering data of a classical Hamiltonian system can be used to decide whether the Hamiltonian function is completely integrable or not. An appropriate infinite set of scattering trajectories is linked together at infinity and the intersection of this sequence of trajectories with a surface in the set of all asymptotes is studied. The plot of these intersections provides the same information as the plots of the usual Poincare sections for bound states do. Numerical examples are given for the scattering of a spinning top, for collisional excitation of an oscillator and a rotator and for potential scattering under the additional influence of an electromagnetic field.

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