Coding of geodesics and Lorenz-like templates for some geodesic flows

TL;DR

This paper constructs a topological template with two ribbons to describe all periodic geodesic orbits on certain hyperbolic orbifolds, using a specific two-letter coding scheme for geodesics.

Contribution

It introduces a novel two-ribbon template and coding method to analyze geodesic flows on orbifolds with three cone points.

Findings

Successfully models all periodic geodesics with the template

Provides a coding scheme for geodesics on hyperbolic orbifolds

Enhances understanding of geodesic flow topology

Abstract

We construct a template with two ribbons that describes the topology of all periodic orbits of the geodesic flow on the unit tangent bundle to any sphere with three cone points with hyperbolic metric. The construction relies on the existence of a particular coding with two letters for the geodesics on these orbifolds.