Warwick Tucker (Uppsala University, Sweden): A rigorous study of short periodic orbits for the Lorenz system

In this talk, we describe a method for finding all short cycles
embedded in a singular-hyperbolic attractor. The method uses a set-valued,
Newton-like operator, applied to specific parts of a Poincare section for
the flow. These specific parts are located by a global search of a trapping
region, obtained by rigorously computed first-return information for the
flow. The situation is complicated by the fact that the attractor is
singular, and hence contains orbits with unbounded return times and
expansion/contraction rates. As an example, we apply our method to the
Lorenz system.