Cusp-scaling behavior in fractal dimension of chaotic scattering
arXiv:nlin/0206022 · doi:10.1103/PhysRevE.65.065201
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.
4 pages, 4 figures, Revtex