English

Les noeuds de Lorenz

Geometric Topology 2016-05-06 v2 Dynamical Systems Number Theory

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.

Keywords

Cite

@article{arxiv.0904.2437,
  title  = {Les noeuds de Lorenz},
  author = {Pierre Dehornoy},
  journal= {arXiv preprint arXiv:0904.2437},
  year   = {2016}
}

Comments

version finale, 59p

R2 v1 2026-06-21T12:51:58.912Z