Epstein class

English Etymology 1 Named for French mathematician Q130087037 Henri Epstein (1932-2024). Noun en mathematics topology A family of real-analytic interval maps that have a particularly well-controlled extension to the complex plane, used to study renormalization, especially for unimodal maps and critical circle maps. en December 1999 Edson de Faria; Welington de Melo Rigidity of critical circle mappings I 10.1007/s100970050011 Journal of the European Mathematical Society 1435-9855 1 4 382 Springer Let r ≥ 3 and let f be a Cr critical circle map with arbitrary irrational rotation number. Then the sequence of renormalizations {ℛn(f)} is bounded in the Cr−1 metric and converges Cr−1 exponentially fast to the Epstein class. en August 2005 Grzegorz Świątek; Genadi Levin Dynamics and Universality of Unimodal Mappings with Infinite Criticality 10.1007/s00220-005-1333-6 Communications in Mathematical Physics 0010-3616 258 1 109 Springer Let us remark that all real bounds of [20] and their proofs hold without any changes for every unimodal map of the form E(|x|ℓ) where E is a diffeomorphism of the Epstein class and ℓ > 1 is any real number. en November 2020 Hao Yang Ji; Si Min Li The Attractor of Fibonacci-like Renormalization Operator 10.1007/s10114-020-9185-8 Acta Mathematica Sinica 1439-8516 36 11 23 Springer The normality of both families comes from Lemma 2.20, Lemma 2.12 and the same argument as in the proof of Proposition 2.14. By Lemma 2.13, any limit map F belongs to the Epstein class Ɛℱα where α = λ/2. en September 2022 Gabriela Estevez; Daniel Smania; Michael Yampolsky Renormalization of Analytic Multicritical Circle Maps with Bounded Type Rotation Numbers 10.1007/s00574-022-00295-8 Bulletin of the Brazilian Mathematical Society 53 3 1054 Springer The Epstein class is a natural class of analytic maps which contains the limit points of renormalizations of smooth maps (see de Melo and van Strien 1993). Etymology 2 By analogy with en ruling class. Coined in early 2026. Proper noun en February 2026 1 en US politics A class of elites in the United States that is associated with Jeffrey Epstein, and possibly involved in his crimes. en 2026-03-02 Astead Herndon; Cameron Peters w:Ro Khanna The “Epstein class,” explained: Why Rep. Ro Khanna isn’t done talking about the Epstein files Vox var(--wikt-palette-darkred) Can you give us a status update [on the Epstein files]? How much is still out there?At least 50 percent still has been hidden, covered up. But what has been released is shocking. [Rep. Thomas] Massie and I didn’t think we’d get this far. They’ve released a fair amount. They’re keeping the worst stuff, but what they’ve released is not a good look at our elite class. It’s not a good look at the Epstein class. https://www.vox.com/podcasts/480850/epstein-files-ro-khanna-accountability-congress-explained https://web.archive.org/web/20260306154025/https://www.vox.com/podcasts/480850/epstein-files-ro-khanna-accountability-congress-explained 2026-03-06 en derogatory collective wealthy and powerful people; billionaires. en 2026-02-11 David Wallace-Wells w:Jon Ossoff Affordability and the ‘Epstein Class’ Will Define American Politics w:The New York Times https://www.nytimes.com/2026/02/11/opinion/billionaires-wealth-tax.html https://web.archive.org/web/20260216100617/https://www.nytimes.com/2026/02/11/opinion/billionaires-wealth-tax.html February 16, 2026 August 21, 2026 Opinion “We were told that MAGA was for working-class Americans,” Senator Jon Ossoff, Democrat of Georgia, said in a speech last weekend. “But this is a government of, by and for the ultrarich. It is the wealthiest cabinet ever. This is the Epstein class, ruling our country.” See also en Epstein's army Epstein coalition Further reading en eponyms