Les noeuds de Lorenz
arXiv:0904.2437 · doi:10.4171/LEM/57-3-1
Abstract
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.
version finale, 59p
References in corpus (1)
Cited by in corpus (7)
- On the zeroes of the Alexander polynomial of a Lorenz knot
- Templates for geodesic flows
- Analytical study of The Lorenz system: existence of infinitely many periodic orbits and their topological characterization
- A Proof of the Conjecture of Lehmer and of the Conjecture of Schinzel-Zassenhaus
- Linking numbers of modular knots
- Kneading the Lorenz attractor
- Partial Classification of Lorenz Knots: Syllable Permutations of Torus Knots Words