Celebratio Mathematica — Williams — Complete Bibliography

Complete Bibliography

Works connected to Okan Gürel

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R. F. Williams: “The bifurcation space of the Lorenz attractor,” pp. 393–399 in Bifurcation theory and applications in scientific disciplines (New York, 31 October–4 November 1977). Edited by O. Gurel and O. E. Roessler. Annals of the New York Academy of Sciences 316. New York Academy of Sciencies, 1979. MR 556844 Zbl 0472.58016 incollection

In a joint paper [1979] John Guckenheimer and the present author showed that the space of the title is two-dimensional, in that the pair \( (k_l,k_r) \) of kneading sequences is a complete conjugacy class invariant for the flows near the three-dimensional Lorenz system. But there are reasons for obtaining more complete knowledge of the space \( \mathcal{K} \) of all such pairs, \( k \). Thus, one can use the “Parry coordinates” \( (\lambda,c) \) but a priori, one doesn’t know these all correspond to Lorenz models — i.e., to differential equations in \( \mathbb{R}^3 \). Secondly, a recurring problem in bifurcation theory is just how do the periodic orbits change. as one changes a bifurcation parameter? Thus we shall present a formula for computing the periodic orbits in terms of the parameter \( k \), i.e., the kneading sequences.

Okan Gürel	Related
Otto E. Rössler	Related