  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.
