2019/08/27 by Michelle Manes, Manes, Michelle, Gabrielle Melamed +3
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1908.10459
openalex publication_date 2019/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Riemann's Existence Theorem gives the following bijections: (1) Isomorphism classes of Belyi maps of degree d. (2) Equivalence classes of generating systems of degree d. (3) Isomorphism classes of dessins d'enfants with d edges. In previous work, the first author and collaborators exploited the correspondence between Belyi maps and their generating systems to provide explicit equations for two infinite families of dynamical Belyi maps. We complete this picture by describing the dessins d'enfants for these two families.