Epstein class

plural Epstein classes

1. mathematicsA 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.

   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).

   2022 September 29, 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

   3 more examples

   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.

   1999 December 29, 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 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.

   2005 August 29, 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

   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.

   2020 November 29, 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

1. USgovernmentA class of elites in the United States that is associated with Jeffrey Epstein, and possibly involved in his crimes.

   1 more example

   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.

   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, archived from the original on 06 Mar 2026

2. UScollectivederogatorygovernmentWealthy and powerful people; billionaires.

   “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.”

   2026 February 11, David Wallace-Wells, quoting Jon Ossoff, “Affordability and the ‘Epstein Class’ Will Define American Politics”, in The New York Times, archived from the original on 16 Feb 2026, Opinion