3 papers
math.DS2025
A study of braids arising from simple choreographies of the planar Newtonian N-body problem
Yuika Kajihara, Eiko Kin, Mitsuru Shibayama
We study periodic solutions of the planar Newtonian -body problem with equal masses. Each periodic solution traces out a braid with strands in 3-dimensional space. When the…
math.GT2024
Agol cycles of pseudo-Anosov maps on the 2-punctured torus and 5-punctured sphere
Jean-Baptiste Bellynck, Eiko Kin
Given a periodic splitting sequence of a measured train track, an Agol cycle is the part that constitutes a period up to the action of a pseudo-Anosov map and the rescaling by its…
math.GT2023
Complete description of Agol cycles of pseudo-Anosov 3-braids
Keiko Kawamuro, Eiko Kin
The equivalence class of an Agol cycle is a conjugacy invariant of a pseudo-Anosov map. Mosher defined train tracks in the torus associated to Farey intervals and investigated the…