The applications ofrenormalization ideas in Dynamical Systems became increasingly popular after 1979, and, since then, they played an important role in the study of several classes of low-dimensional systems.

Very roughly speaking, the philosophy of renormalization is that, after appropriate rescalings, the long time behaviors at short scales of certain systems are dictated by other systems within a fixed class S of systems.In particular,such a renormalization procedure can iterated and, as it turns out, the phrase portraits of those systems whose successive renormalizations tend to stay in a compact portion of S can often be reasonably described ("plough in the dynamical plane to harvest in the parameter space",A. Douady).