Anomalous oscillations of average transient lifetimes near crises
  It is common that the average length of chaotic transients appearing as a consequence of crises in dynamical systems obeys a power low of scaling with the distance from the crisis point. It is, however, only a rough trend; in some cases considerable oscillations can be superimposed on it. In this letter we report anomalous oscillations due to the intertwined structure of basins of attraction. We also present a simple geometrical model that gives an estimate of the period and amplitude of these oscillations. The results obtained within the model coincide with those yielded by computer simulations of a kicked spin model and the Henon map. 
Krzysztof Kacperski and Janusz A. Holyst