2024/10/26 by Matthieu Astorg, Astorg, Matthieu, Davoud Cheraghi +3
Mathematics · Physics and Astronomy · #34F46 (Secondary) #37F10 (Primary) #Advanced Algebra and Geometry #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2410.20179
openalex publication_date 2024/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We prove that cubic polynomial maps with a fixed Siegel disk and a critical orbit eventually landing inside that Siegel disk lie in the support of the bifurcation measure. This answers a question of Dujardin in positive. Our result implies the existence of holomorphic disks in the support of the bifurcation measure, and also implies that the set of rigid parameters is not closed in the moduli space of cubic polynomials.