Chaotic scattering off the magnetic dipole

Fractal scattering in a radiation field

“…This fractal set of singularities occurs when the incoming particle asymptotes intersect the tangles of the invariant manifolds in the asymptotic region. The recipe for extracting information about chaotic scattering processes and the underlying fractal structure that governs that dynamics has been developed by Jung and others for a variety of model systems [1][2][3][4][5]. The method described here for obtaining the underlying fractal structure for chaotic scattering process can also be applied to scattering processes in the absence of a radiation field, as has been shown in Ref.…”

Chaotic scattering in the restricted three-body problem I. The Copenhagen problem

“…For J < JL2 = JL3 = --6.913o.. the Hill curves enclose regions of pure bound motion in the form of effective potential barriers; for JL4 > J > JL2 such barriers also exist but do not isolate regions of bounded motion (Szebehely, 1967). Today is quite clear that the key to the understanding of chaotic scattering is the chaotic saddle (Jung and Scholz, 1987). For the latter to occur, not only must the number of unstable periodic orbits be infinite, but homoclinic and heteroclinic connections between them have to exist .…”

“…The variety of systems studied is very rich implying that chaotic scattering is a widespread phenomenon. Examples are billiard systems (Eckhardt, 1987;Gaspard and Rice, 1989;Meyer et al, 1995), models of potential scattering (Eckhardt and Jung, 1986;Jung andScholz, 1987, 1988;Bleher et al, 1989), inelastic molecular scattering (Brumer and Shapiro, 1988), reactive scattering (Noid et al, 1986), soliton scattering (Campbell et al, 1986) and hydrodynamic open flow (Jung and Ziemniak, 1992;Prntek et al, 1995). For recent reviews on the subject see Smilansky (1992) and the special issue of the journal CHAOS (num., 4, 1993).…”

“…Based on the chart for the symmetric periodic orbits by Hrnon (1965a), the parameter space is divided in regions which are basically distinguished by a geometric property of these orbits, namely, whether there exist or not periodic orbits which cross the segment that joins the stars. As will be shown later, these periodic orbits correspond to the so called primitive periodic orbits, which are the basic periodic orbits which characterize the chaotic saddle (Jung and Scholz, 1987). Sections 3 to 5 are devoted to describe separately the scattering motion of the parameter space regions previously introduced.…”

The vibrational dynamics of 3D HOCl above dissociation

“…This fractal set of singularities occurs when the incoming particle asymptotes intersect the tangles of the invariant manifolds in the asymptotic region. The recipe for extracting information about chaotic scattering processes and the underlying fractal structure that governs that dynamics has been developed by Jung and others for a variety of model systems [9][10][11][12][13]33]. The method described here for obtaining the underlying fractal structure for chaotic scattering process can also be applied to scattering processes in the absence of a radiation field, as has been shown in [14] where the chaotic scattering dynamics of a molecular system is analysed.…”