Japanese Journal of Mathematics

, Volume 4, Issue 1, pp 47–61

Right-handed vector fields & the Lorenz attractor


DOI: 10.1007/s11537-009-0854-8

Cite this article as:
Ghys, É. Jpn. J. Math. (2009) 4: 47. doi:10.1007/s11537-009-0854-8


The main purpose of this paper is to introduce a class of vector fields on the 3-sphere that we call “right-handed”. Roughly speaking, they are characterized by the fact that any two orbits link positively. We give various natural examples and provide some kind of homological characterization. We then describe some of the main dynamical properties of these flows.

Keywords and phrases:

dynamical systems Lorenz attractor positive braids 

Mathematics Subject Classification (2000):

37C70 57M25 

Copyright information

© The Mathematical Society of Japan and Springer Japan 2009

Authors and Affiliations

  1. 1.Unité de Mathématiques, Pures et Appliquées, de l’ École Normale Supérieure de Lyon, U.M.R. 5669 du Centre national de la recherche scientifiqueLyon Cedex 07France

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