Abstract
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 (and their associated scaling exponents) are parametrized by a “modulus of discontinuity,” μ, measuring the difference in dth derivatives, as well as the degree d. The asymptotic behavior in the limit d→1+ is also determined.
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