A renormalization fixed point for Lorenz maps
arXiv:0908.0723 · doi:10.1088/0951-7715/23/6/003
Abstract
A Lorenz map is a Poincaré map for a three-dimensional Lorenz flow. We describe the theory of renormalization for Lorenz maps with a critical point and prove that a restriction of the renormalization operator acting on such maps has a hyperbolic fixed point. The proof is computer assisted and we include a detailed exposition on how to make rigorous estimates using a computer as well as the implementation of the estimates.
29 pages, 2 figures