A wide class of deterministic integer maps exhibit transient behavior which can be described in universal fashion. For the cases which in the continuum limit correspond to bifurcations, transients consist of two regimes, sharply separated by a crossover point which displays universal scaling with the size of the set. Moreover, their average lengths display power-law dependence on the accuracy of their measurement. This scaling behavior persists away from neutrally stable points but with logarithmic dependence on the size of the set.

• Received 24 June 1985

DOI:https://doi.org/10.1103/PhysRevA.32.3768