Review and examples of non-Feigenbaum critical situations associated with period-doubling

We review several critical situations, linked with period-doubling transition to chaos, which require using at least two-dimensional maps as models representing the universality classes. Each of them corresponds to a saddle solution of the two-dimensional generalization of Feigenbaum-Cvitanovic equation and is characterized by a set of distinct universal constants analogous to Feigenbaum´s α and δ. We present a number of examples (driven self-oscillators, coupled Henon-like maps, coupled driven oscillators, coupled chaotic self-oscillators), which manifest these types of behavior.