Theory of oscillations in average crisis-induced transient lifetimes

Analytical and numerical study of the roughly periodic oscillations emerging on the background of the well-known power law governing the scaling of the average lifetimes of crisis induced chaotic transients is presented. The explicit formula giving the amplitude of “normal” oscillations in terms of the eigenvalues of unstable orbits involved in the crisis is obtained using a simple geometrical model. We also discuss the commonly encountered situation when normal oscillations appear together with “anomalous” ones caused by the fractal structure of basins of attraction.