Right-handed vector fields & the Lorenz attractor
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
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- 2.V.I. Arnold and B.A. Khesin, Topological Methods in Hydrodynamics, Appl. Math. Sci., 125, Springer-Verlag, New York, 1998.Google Scholar
- 4.D. DeTurck and H. Gluck, The Gauss linking integral on the 3-sphere and in hyperbolic 3-space, e-print, arXiv:math.GT/0406276.Google Scholar
- 7.É. Ghys, Knots and dynamics, In: International Congress of Mathematicians. Vol. I, Eur. Math. Soc., Zürich, 2007, pp. 247–277.Google Scholar