Transition to chaotic scattering: Signatures in the differential cross section

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6 Citations (Scopus)


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 languageEnglish
Article number046204
Number of pages6
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number4
Publication statusPublished - Oct 2008


  • open hydrodynamical flows
  • rainbow scattering


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