Les noeuds de Lorenz

Pierre Dehornoy (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

This article is a survey on Lorenz knots. We describe the original construction, prove several classical properties, in particular the fact that the closure of a positive braid is a fibered knot, and describe Ghys'correspondance between modular knots and Lorenz knots. We also prove two new properties, namely that following Ghys' correspondance, the images of trivial orbits of the Lorenz flow form a subgroup of the class group, and that the reverse images of an element in the class group and of its inverse are isotopic orbits.

Mots clés: Noeuds; attracteur étrange

Domaines: Topologie géométrique [math.GT]; Systèmes dynamiques [math.DS]; Théorie des nombres [math.NT]

Pierre Dehornoy. Les noeuds de Lorenz. L'Enseignement Mathématique , 2011, 57, pp.211-280. ⟨hal-00375709v2⟩