Influence of asymmetry on multifractal properties of maps

It is shown that the multifractal properties of a period-doubling attractor and of repellers associated with symmetric unimodal maps are affected if an asymmetry is introduced in the zth derivative of the map at its maximum of order z. For a quadratic map, a universal scaling factor associated with the period-doubling attractor is calculated as a function of an asymmetry parameter. Expansions of multifractal functions in terms of an asymmetry parameter are obtained.