Different types of scaling in the dynamics of period-doubling maps under external periodic driving (Q5930226)

The authors discuss the scaling properties of the parameter space for the perturbed logistic map \(x\mapsto \lambda-x^ 2+\varepsilon \cos(2\pi\omega+\phi)\). The parameter \(\lambda\) is taken close to the Feigenbaum critical point and the perturbation amplitude \(\varepsilon\) is small. Different types of scaling are observed for rational and irrational frequency \(\omega\). The scaling properties are illustrated by parameter plane diagrams for a rescaled Lyapunov exponent.