Transition to chaotic scattering: Signatures in the differential cross section

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 languageEnglish
Article number046204
Number of pages6
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume78
Issue number4
DOIs
Publication statusPublished - Oct 2008

Keywords

  • open hydrodynamical flows
  • rainbow scattering

Cite this

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title = "Transition to chaotic scattering: Signatures in the differential cross section",
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.",
keywords = "open hydrodynamical flows, rainbow scattering",
author = "A. Schelin and {de Moura}, {Alessandro Paula Servio} and Celso Grebogi",
year = "2008",
month = "10",
doi = "10.1103/PhysRevE.78.046204",
language = "English",
volume = "78",
journal = "Physical Review. E, Statistical, Nonlinear and Soft Matter Physics",
issn = "1539-3755",
publisher = "AMER PHYSICAL SOC",
number = "4",

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T1 - Transition to chaotic scattering

T2 - Signatures in the differential cross section

AU - Schelin, A.

AU - de Moura, Alessandro Paula Servio

AU - Grebogi, Celso

PY - 2008/10

Y1 - 2008/10

N2 - 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.

AB - 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.

KW - open hydrodynamical flows

KW - rainbow scattering

U2 - 10.1103/PhysRevE.78.046204

DO - 10.1103/PhysRevE.78.046204

M3 - Article

VL - 78

JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

SN - 1539-3755

IS - 4

M1 - 046204

ER -