Scaling of the Lyapunov exponent in type-III intermittent chaos

The scaling behaviour of the Lyapunov exponent near the transition to chaos via type-III intermittency is determined for a generic map. 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 contrasts with earlier predictions for the scaling behaviour of the Lyapunov exponent in type-III intermittency.