2024/11/20 by Sylvain Crovisier, Crovisier, Sylvain, Mikhail Lyubich +5
Engineering · Mathematics · #37C05 (secondary) #37E20 (primary) 37E30 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2411.13624
openalex publication_date 2024/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We formulate and prove a priori bounds for the renormalization of Hénon-like maps (under certain regularity assumptions). This provides a certain uniform control on the small-scale geometry of the dynamics, and ensures pre-compactness of the renormalization sequence. In a sequel to this paper, a priori bounds are used in the proof of the main results, including renormalization convergence, finite-time checkability of the required regularity conditions and regular unicriticality of the dynamics.