Fractal Basin Boundaries
Dissipative dynamical systems often possess multiple coexisting attractors. The set of initial conditions leading to trajectories landing on an attractor is the basin of attraction of this attractor. Each attractor thus has its own basin, which is invariant under the dynamics, since images of every point in the basin still belong to the same basin. The basins of attraction are separated by boundaries. We shall demonstrate that it is common for nonlinear systems to have fractal basin boundaries, the dynamical reason for which is nothing but transient chaos on the boundaries. In fact, fractal basin boundaries contain one or several nonattracting chaotic sets.