A renormalization fixed point for Lorenz maps
Dynamical Systems
2014-12-30 v2
Abstract
A Lorenz map is a Poincar\'e 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.
Keywords
Cite
@article{arxiv.0908.0723,
title = {A renormalization fixed point for Lorenz maps},
author = {Björn Winckler},
journal= {arXiv preprint arXiv:0908.0723},
year = {2014}
}
Comments
29 pages, 2 figures