Lyapunov exponent for type-III intermittent chaos

The behaviour of the Lyapunov exponent near the transition to chaos via type-III intermittency is numerically determined for a generic map showing this transition. A critical exponent β expressing the scaling of the Lyapunov exponent as a function of both, the reinjection probability and the nonlinearity of the map is calculated. It is found that the critical exponent varies on the interval 0 < β < 1 . This extends earlier predictions for the scaling behaviour of the Lyapunov exponent in type-III intermittency.