Cusp-scaling behavior in fractal dimension of chaotic scattering

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

doi:10.1103/PhysRevE.65.065201

Cusp-scaling behavior in fractal dimension of chaotic scattering

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

Physics

Research output: Contribution to journal › Article › peer-review

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 language	English
Article number	065201
Pages (from-to)	-
Number of pages	4
Journal	Physical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume	65
Issue number	6
DOIs	https://doi.org/10.1103/PhysRevE.65.065201
Publication status	Published - Jun 2002

Keywords

BIFURCATION
SYSTEMS

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10.1103/PhysRevE.65.065201

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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.",

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AU - Lai, Ying-Cheng

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AB - 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.

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KW - SYSTEMS

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DO - 10.1103/PhysRevE.65.065201

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Cusp-scaling behavior in fractal dimension of chaotic scattering

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Keywords

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