On the universality class dependence of period doubling indices

The dependence on ? of the period doubling scaling indices for unimodal maps with a critical point of the form| x| ? is numerically investigated. A new symbolic dynamics based computation technique working in configuration space is introduced. The existence of an upper bound for ? (?->?) is numerically verified. An accurate estimate of 29.8 is given for this limit. Moreover, the global functional form of ? (?) is shown to have an interesting symmetry.