Cusp-scaling behavior in fractal dimension of chaotic scattering

A E Motter, Y C Lai, Ying-Cheng Lai

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Abstract

A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal dimension of the chaotic set for such a bifurcation. Our analysis and numerical computations in both two- and three-degrees-of-freedom systems suggest a striking feature associated with these subtle bifurcations: the dimension typically exhibits a sharp, cusplike local minimum at the bifurcation.

Original languageEnglish
Article number065201
Pages (from-to)-
Number of pages4
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume65
Issue number6
DOIs
Publication statusPublished - Jun 2002

Keywords

  • BIFURCATION
  • SYSTEMS

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