Renormalization of asymmetric unimodal maps

We carry out a renormalization analysis for unimodal maps possessing a degree-d critical point with differing left and right dth derivatives. More precisely, we prove, using Herglotz function techniques, the existence of a family of period-two points of the Feigenbaum renormalization operator. These universal functions land their associated scaling exponents) are parametrized by a "modulus of discontinuity", mu, measuring the difference in dth derivatives, as well as the degree d. The asymptotic behaviour in the Limit d --> 1+ is also determined.