Dependence of universal constants upon multiplication period in nonlinear maps

Noninvertible one-dimensional maps with cycle periods undergoing multiplication by a factor N, as a result of (tangent) bifurcation, are governed by map-independent universal constants αN${\alpha }_N$,δN${\delta }_N$ as the parameter λ of the map approaches the point of accumulation λN∞${\lambda }_{N\infty }$. By explicit computation, we have determined the constants for all cycle structures and all values of N up to 7 (and in addition for many cycles up to N=11). We find that the relation between α and δ is roughly independent of the detailed cycle structure and follows quite well the Eckmann-Epstein-Wittwer asymptotic prediction that 3δ=2α2$\alpha 2$. .AE