title: Catastrophe of riddling
abstract: Most existing works on riddling assume that the underlying dynamical system possesses an invariant subspace. We find that, under arbitrarily small, deterministic perturbations, a riddled basin is typically destroyed and replaced by fractal ones, a catastrophe of riddling. We elucidate, based on analyzing unstable periodic orbits, the dynamical mechanism of the catastrophe. Analysis of the critical behaviors leads to the finding of a transient chaotic behavior that is different from those reported previously.
authors.affiliation: Department of Mathematics, Department of Electrical Engineering, and Department of Physics, Center for Systems Science and Engineering Research, Arizona State University, Tempe, Arizona 85287, USA.
authors.initials: YC
authors.lastname: Lai