Abrupt bifurcation to chaotic scattering with discontinuous change in fractal dimension

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Abstract

One of the major routes to chaotic scattering is through an abrupt bifurcation by which a nonattracting chaotic saddle is created as a system parameter changes through a critical value. In a previously investigated case, however, the fractal dimension of the set of singularities in the scattering function changes continuously through the bifurcation. We describe a type of abrupt bifurcation to chaotic scattering where this physically relevant dimension changes discontinuously at the bifurcation. The bifurcation is illustrated using a class of open Hamiltonian systems consisting of Morse potential hills.

Original languageEnglish (US)
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume60
Issue number6 A
StatePublished - Dec 1999

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Fractal Dimension
fractals
Bifurcation
Scattering
Morse potential
scattering functions
saddles
scattering
routes
Morse Potential
Open Systems
Saddle
Hamiltonian Systems
Critical value
Singularity

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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title = "Abrupt bifurcation to chaotic scattering with discontinuous change in fractal dimension",
abstract = "One of the major routes to chaotic scattering is through an abrupt bifurcation by which a nonattracting chaotic saddle is created as a system parameter changes through a critical value. In a previously investigated case, however, the fractal dimension of the set of singularities in the scattering function changes continuously through the bifurcation. We describe a type of abrupt bifurcation to chaotic scattering where this physically relevant dimension changes discontinuously at the bifurcation. The bifurcation is illustrated using a class of open Hamiltonian systems consisting of Morse potential hills.",
author = "Ying-Cheng Lai",
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language = "English (US)",
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AB - One of the major routes to chaotic scattering is through an abrupt bifurcation by which a nonattracting chaotic saddle is created as a system parameter changes through a critical value. In a previously investigated case, however, the fractal dimension of the set of singularities in the scattering function changes continuously through the bifurcation. We describe a type of abrupt bifurcation to chaotic scattering where this physically relevant dimension changes discontinuously at the bifurcation. The bifurcation is illustrated using a class of open Hamiltonian systems consisting of Morse potential hills.

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