2019/09/13 by Mauricio Garay, Garay, Mauricio, Duco van Straten +1
Mathematics · Physics and Astronomy · #70H08 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1909.06053
openalex publication_date 2019/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a new type of normal form at a critical point of an analytic Hamiltonian. Under a Bruno condition on the frequency, we prove a convergence statement to the normal form. Using this result, we prove the Herman invariant tori conjecture namely the existence of a positive measure set of invariant tori near the critical point. This paper is an update of the first 2012 proof of the author. The functional analytic arguments have been simplified using Banach functors, minor points have been clarified. A series of videos is available on the webpage https://www.agtz.mathematik.uni-mainz.de/category/alg-geom/