Lorentz Attractors, Topology and Modular Flows
Published on 11 May 2007 at 3:11 am.
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While working with POV Ray, I stumbled on this great article from the American Mathematical Society’s Monthly Essays. This article examines the Lorenz attractor and its periodic orbits. It turns out that the periodic orbits form knots, but not just any knots. They comprise only a very small subset of possible knots.
The article continues to examine modular flows on lattices, and the periodic orbits that result. It turns out that the knots defined by these periodic orbits on the modular flow coincide with the Lorenz knots!
Kevin Knuth
Albany NY
