Celebratio Mathematica — Williams

My collaboration with Bob Williams

Works connected to Tudor Ștefan Rațiu

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R. F. Williams: “The structure of Lorenz attractors,” pp. 94–112 in Turbulence seminar (Berkeley, CA, 1976–1977). Edited by P. Bernard and T. Ratiu. Lecture Notes in Mathematics 615. Springer (Berlin), 1977. Lecture VII. With appendix “Computer pictures of the Lorenz attractor.”. This appears to have been adapted for an article published in Inst. Hautes Études Sci. Publ. Math. 50 (1979). MR 461581 Zbl 0363.58005 incollection

The system of equations \begin{align*} \dot{x} &= -10x + 10y \\ \dot{y} &= 28x -y - xz \\ \dot{z} &= -\frac{8}{3}z + xy \end{align*} of E. N. Lorenz has attracted much attention lately, in part because of its supposed relation to turbulence. As was mentioned in [Marsden 1977], it is obtained by the truncation of the Navier–Stokes Equation. How this system really relates to turbulene is not known. yet and — as we saw in earlier talks — there are many pros and cons for this. One thing is sure: this system certainly gives rise to a type of attractor which is nonclassical and not even strange in the sense of Smale [1977]. Notice that according to the bifurcation classification of [Marsden 1977], the system above gives rise to the “standard” Lorenz attractor and the goal of this lecture is to study it.

Peter Simon Bernard	Related
Tudor Ștefan Rațiu	Related