A VARIETY OF PERIOD-DOUBLING UNIVERSALITY CLASSES IN MULTIPARAMETER ANALYSIS OF TRANSITION TO CHAOS

In multi-parameter analysis of the onset of chaos non-Feigenbaum perio d-doubling behavior may occur at some special paths in the parameter s pace. There are two possibilities: (i) the dynamics at the on rer of c haos remains essentially one-dimensional, but the one-dimensional map is distorted in such a way that leaves Feigenbaum's universality class , (ii) a new mode comes to the threshold of instability and increases the effective dimension of the dynamics. We submit a list of one-dimen sional and two-dimensional maps which represent distinct classes of th e period-doubling universality, discuss the properties of the associat ed types of critical behavior at the border of chaos, and demonstrate pictures of the universal parameter space arrangement near the critica l points.