Cusp-scaling behavior in fractal dimension of chaotic scattering.
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.
Department of Mathematics, Center for Systems Science and Engineering Research, Arizona State University, Tempe, AZ 85287, USA.
Adilson E
AE
Motter
Ying-Cheng
YC
Lai