Real Analysis Exchange

A Short Proof of the Existence of Universal Functions

Benjamin D. Mestel

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Abstract

We present a short proof of the existence of universal functions for period-doubling and critical golden-mean circle maps for all degrees of criticality \(d \gt 1\). The method is based on H. Epstein's Herglotz-function technique.

Article information

Source
Real Anal. Exchange, Volume 38, Number 2 (2012), 425-430.

Dates
First available in Project Euclid: 27 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.rae/1403894902

Mathematical Reviews number (MathSciNet)
MR3261887

Subjects
Primary: 37E20: Universality, renormalization [See also 37F25] 37E05: Maps of the interval (piecewise continuous, continuous, smooth) 37E10: Maps of the circle

Keywords
Feigenbaum functional equation Herglotz function universality

Citation

Mestel, Benjamin D. A Short Proof of the Existence of Universal Functions. Real Anal. Exchange 38 (2012), no. 2, 425--430. https://projecteuclid.org/euclid.rae/1403894902


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