Abstract
We show that bifurcations in chaotic scattering manifest themselves through the appearance of an infinitely fine-scale structure of singularities in the cross section. These "rainbow singularities" are created in a cascade, which is closely related to the bifurcation cascade undergone by the set of trapped orbits (the chaotic saddle). This cascade provides a signature in the differential cross section of the complex pattern of bifurcations of orbits underlying the transition to chaotic scattering. We show that there is a power law with a universal coefficient governing the sequence of births of rainbow singularities and we verify this prediction by numerical simulations.
Original language | English |
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Article number | 046204 |
Number of pages | 6 |
Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |
Volume | 78 |
Issue number | 4 |
DOIs | |
Publication status | Published - Oct 2008 |
Keywords
- open hydrodynamical flows
- rainbow scattering