Chaotic scattering off the magnetic dipole

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Abstract
Classical scattering with singularities of Cantor-set type can be observed if unstable localised orbits exist whose homoclinic structures are transported to infinity by the Hamiltonian flow. An electron moving in the field of a magnetic dipole is a simple example of physical relevance to demonstrate this transport mechanism. In the asymptotic plane spanned by impact parameter and incoming direction the deflection function is singular for initial conditions leading to captured orbits. Using the method of Poincare sections, the authors find a correspondence between this set of singularities and the stable manifolds of localised orbits. The scattering data which are measured in the asymptotic region of free motion provide information about chaotic motion in a finite part of the position space.

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