Cusp-scaling behavior in fractal dimension of chaotic scattering

Details Cusp-scaling behavior in fractal dimension of chaotic scattering Cusp-scaling behavior in fractal dimension of chaotic scattering

2002-06-13

arxiv.org/abs/nlin/0206022v1

Phys. Rev. E 65, 065201(R) (2002)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 4 figures, Revtex

Scientific paper

10.1103/PhysRevE.65.065201

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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