We treat a chaotic Hamiltonian scattering system with three degrees of freedom where the chaotic invariant set is of low dimension. Then the chaos and its structure are not visible in scattering functions plotted along one-dimensional lines in the set of asymptotic initial conditions. We show that an asymptotic observer can nevertheless see the structure of the chaotic set in an appropriate scattering function on the two-dimensional impact parameter plane and in the doubly differential cross section. Rainbow singularities in the cross section carry over the symbolic dynamics of the chaotic set into the cross section. A smooth image of the fractal structure of the chaotic set can be reconstructed on the domain of the cross section.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - Aug 12 2014|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics