Cusp-scaling behavior in fractal dimension of chaotic scattering

Adilson E. Motter, Ying-Cheng Lai

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 (US)
Article number065201
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume65
Issue number6
DOIs
StatePublished - Jun 2002

Fingerprint

Scaling Behavior
Cusp
cusps
Fractal Dimension
fractals
Bifurcation
Scattering
scaling
scattering
scaling laws
topology
degrees of freedom
orbits
Scaling Laws
Invariant Set
Local Minima
Numerical Computation
Periodic Orbits
Unstable
Degree of freedom

ASJC Scopus subject areas

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

Cite this

Cusp-scaling behavior in fractal dimension of chaotic scattering. / Motter, Adilson E.; Lai, Ying-Cheng.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 65, No. 6, 065201, 06.2002.

Research output: Contribution to journalArticle

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