Epstein class

Named for French mathematician Henri Epstein (Q130087037) (1932-2024).

Epstein class (plural Epstein classes)

1. (mathematics, topology) This term needs a definition. Please help out and add a definition, then remove the text {{rfdef}}.
   • 1999 December, Edson de Faria, Welington de Melo, “Rigidity of critical circle mappings I”, in Journal of the European Mathematical Society, volume 1, number 4, Springer, →DOI, →ISSN, page 382:

     Let r ≥ 3 and let f be a C^r critical circle map with arbitrary irrational rotation number. Then the sequence of renormalizations {ℛⁿ(f)} is bounded in the C^r−1 metric and converges C^r−1 exponentially fast to the Epstein class.

   • 2005 August, Grzegorz Świątek, Genadi Levin, “Dynamics and Universality of Unimodal Mappings with Infinite Criticality”, in Communications in Mathematical Physics, volume 258, number 1, Springer, →DOI, →ISSN, page 109:

     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.

   • 2020 November, Hao Yang Ji, Si Min Li, “The Attractor of Fibonacci-like Renormalization Operator”, in Acta Mathematica Sinica, volume 36, number 11, Springer, →DOI, →ISSN, page 23:

     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 Ɛℱ_α where α = λ/2.

   • 2022 September, Gabriela Estevez, Daniel Smania, Michael Yampolsky, “Renormalization of Analytic Multicritical Circle Maps with Bounded Type Rotation Numbers”, in Bulletin of the Brazilian Mathematical Society, volume 53, number 3, Springer, →DOI, page 1054:

     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).

By analogy with ruling class. Coined in early 2026.

the Epstein class (US politics)

1. A class of elites in the United States that is associated with Jeffrey Epstein, and possibly involved in his crimes.
   • 2026 March 2, Astead Herndon, Cameron Peters, quoting Ro Khanna, “The “Epstein class,” explained: Why Rep. Ro Khanna isn’t done talking about the Epstein files”, in Vox‎^[1], archived from the original on 6 March 2026:

     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.

2. (derogatory, collective) Wealthy and powerful people; billionaires.
   • 2026 February 11, David Wallace-Wells, quoting Jon Ossoff, “Affordability and the ‘Epstein Class’ Will Define American Politics”, in The New York Times, 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.”

• Epstein class on Wikipedia.Wikipedia