Renormalization of asymmetric unimodal maps

Osbaldestin, A. H.; Mestel, B. D.
February 2000
AIP Conference Proceedings;2000, Vol. 502 Issue 1, p369
Academic Journal
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. © 2000 American Institute of Physics.


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