Intermingled basins and on-off intermittency in a multistate system.

We consider a dynamical system containing infinite low-dimensional symmetric invariant subspaces, each of which has a chaotic state. Intermingled basins are found between these multiple chaotic states when they are stable in the subspaces. As a parameter of the system varies, the largest Lyapunov exponent transverse to the invariant subspace can change from negative to positive; then, the system dynamics changes from an intermingled basin state to a multistate on-off intermittency. The statistical behavior and physical transportation property for different dynamic states are investigated in detail.