Transition to chaotic scattering: signatures in the differential cross section.
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.
Schelin
Adriane B
AB
Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970, São Paulo, São Paulo, Brazil. schelin@if.usp.br
de Moura
Alessandro P S
AP
Grebogi
Celso
C