Work

Bounds on saddle connections for flat spheres

Year: 2026

Type: article

Abstract: We consider a flat metric with conical singularities on the sphere. Under the assumption that no partial sum of angle defects is equal to , we draw on the geometry of immersed disks to obtain an explicit upper bound on the number of saddle connections with at most self‐intersections. Additionally, we establish an upper bound on their lengths for a surface with a normalized area. Finally, we apply these bounds to the counting of singular trajectories in irrational polygonal billiards.

Source: Journal of Topology

DOI: 10.1112/topo.70076

Authors: Kai Fu, Guillaume Tahar

Institutions: Max Planck Institute for Mathematics in the Sciences, Beijing Institute of Mathematical Sciences and Applications

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Natural Science Foundation of Beijing Municipality

Awards: G3746020814, Moduli spaces of Differentials: Flat surfaces and interactions