Fine structure in the scaling of type-I intermittency bifurcations

Tangent bifurcations in maps with type-I intermittency have been studied numerically and oscillations in the statistical properties were found as functions of the control parameter. The average length of laminar events, the Lyapunov exponent and the averages of the dynamical variable were calculated for quadratic and quartic normal form tangencies. In addition to the exponents of the monotonic critical behavior, the frequency of the oscillations is also simply related to the nonlinear term of the maps.