Studying a simple ODE, Lorenz discovered in 1963 an object that is called today a strange attractor: nearby points are attracted to a set of fractal dimension, and move around this set chaotically, with sensitive dependence on initial conditions.Understanding this attractor was one of the 18 problems for the twenty-first century proposed by Fields medalist Steven Smale. Namely: "Is the dynamics of the ordinary differential equations of Lorenz that of the geometric Lorenz attractor of Williams, Guckenheimer, and Yorke?"
Warwick Tucker answered this question in the affirmative in his PhD thesis (1998). His technical proof makes use of a combination of normal form theory and validated interval arithmetic.
