2017/07/17 by Jonguk Yang, Yang, Jonguk
Mathematics · Physics and Astronomy · #32H50 (secondary) #37F25 (primary) #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.1707.04997
openalex publication_date 2017/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It was recently shown by Gaidashev and Yampolsky that appropriately defined renormalizations of a sufficiently dissipative golden-mean semi-Siegel Hénon map converge super-exponentially fast to a one-dimensional renormalization fixed point. In this paper, we show that the asymptotic two-dimensional form of these renormalizations is universal, and is parameterized by the average Jacobian. This is similar to the limit behavior of period-doubling renormalization in the Hénon family considered by de Carvalho, Lyubich and Martens. As an application of our result, we prove that the boundary of the golden-mean Siegel disk of a dissipative Hénon map is non-rigid.