A new view of the Lorenz attractor
The scenario of appearance of the Lorenz attractor is studied. The authors propose a method, which allows to reduce the problem of finding unstable periodic orbits to the one-dimensional case. Using this method they show the erroneous of some elements of ``traditional'' view on the scenario for the attractor birth. In particular, they show that at \(r=r_1=13.9266\dots\) (\(\sigma=10\), \(b=8/3\)) the separatrices \(\Gamma_1\) and \(\Gamma_2\) resulting from an origin do not form homoclinic loops. Respectively, the mechanism of the birth of unstable limit cycles in Lorenz systems is reconsidered.
scientific article; zbMATH DE number 1915966