Intermingled basins and two-state on-off intermittency

We consider dynamical systems which possess two low-dimensional symmetric invariant subspaces. In each subspace, there is a chaotic attractor, and there are no other attractors in the phase space. As a parameter of the system changes, the largest Lyapunov exponents transverse to the invariant subspaces can change from negative to positive: the former corresponds to the situation where the basins of the attractors are intermingled, while the latter corresponds to the case where the system exhibits a two-state on-off intermittency. The phenomenon is investigated using a physical example where particles move in a two-dimensional potential, subjected to friction and periodic forcing.