On the shape and dimension of the Lorenz attractor

Abstract

It is shown how the global attractor of the Lorenz equations is contained in a volume bounded by a sphere, a cylinder, the volume between two parabolic sheets, an ellipsoid and a cone. The first four are absorbing volumes while the interior of the cone is expelling. By a numerical search over these volumes, it is found that the origin is the most unstable point on the attractor and that an upper bound for the attractor's Lyapunov dimension is 2.401 when b = 8/3, r = 28 and a = 10.