Dessins d'Enfants for Single-Cycle Belyi Maps
Michelle Manes, Gabrielle Melamed, Bella Tobin

TL;DR
This paper explores the connection between Belyi maps and dessins d'enfants, providing explicit descriptions for two infinite families of dynamical Belyi maps, thereby enriching the understanding of their combinatorial and algebraic structures.
Contribution
It completes the classification by explicitly describing dessins d'enfants for two previously studied families of dynamical Belyi maps.
Findings
Explicit dessins d'enfants for two infinite families of Belyi maps.
Enhanced understanding of the combinatorial structures of these maps.
Strengthened link between Belyi maps and dessins d'enfants.
Abstract
Riemann's Existence Theorem gives the following bijections: (1) Isomorphism classes of Belyi maps of degree . (2) Equivalence classes of generating systems of degree . (3) Isomorphism classes of dessins d'enfants with 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Advanced Algebra and Geometry
