2009/08/31 by Björn Winckler
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Chaos control and synchronization #Exposition (narrative) #Fixed point #Lorenz system #Mathematical Dynamics and Fractals #Operator (biology) #Renormalization #Renormalization group #math.DS #msc:37E20
paper · pdf · doi:10.1088/0951-7715/23/6/003
29 pages, 2 figures
arxiv created 2010/03/14 · openalex publication_date 2010/04/29 · arxiv updated 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.