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Cusp-scaling behavior in fractal dimension of chaotic scattering

Adilson E. Motter·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.

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Adilson E. Motter, Ying-Cheng Lai. 2002-06-13. Cusp-scaling behavior in fractal dimension of chaotic scattering. https://doi.org/10.1103/physreve.65.065201

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