, Volume 4, Issue 1, pp 47-61

Right-handed vector fields & the Lorenz attractor

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Abstract.

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.

Communicated by: Toshiyuki Kobayashi
This article is based on the 5th Takagi Lectures that the author delivered at the University of Tokyo on October 4 and 5, 2008.